Physics
107 Solved Past Papers
2014 – 2024 Archives
Waves Past Papers
Solved past paper MCQs for Waves from official UHS, NUMS, SZABMU, DUHS, and KMU examinations. Includes verified distractor autopsies and step-by-step cognitive explanations.
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By increasing the temperature of medium about \( 1 ^\circ\text{C} \), the speed of sound is increased up to [SZABMU 2024]
A
\( 0.41 \text{ ms}^{-1} \)
B
\( 0.51 \text{ ms}^{-1} \)
C
\( 0.61 \text{ ms}^{-1} \)
D
\( 0.71 \text{ ms}^{-1} \)
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Temperature directly increases the kinetic activity of gas molecules, allowing sound pressure waves to transmit faster.
Formula:
$$ v_t \approx v_0 + 0.61t $$
Solution:
The empirical and theoretically derived formula shows a linear dependency near standard room temperatures.
The constant coefficient reveals that for every single degree Celsius (\( 1 ^\circ\text{C} \)) rise in temperature, the speed of sound in air increases by exactly \( 0.61 \text{ m/s} \).
Why other options are incorrect:
Options A, B, and D provide completely incorrect mathematical constants for standard air mixtures.
What will be the fundamental frequency in a stretched string, when its is plucked at central point while it has a speed of \( 48 \text{ ms}^{-1} \) with string length of 8m? [SZABMU 2024]
A
3 Hz
B
6 Hz
C
9 Hz
D
12 Hz
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Plucking a string exactly at its center forces the center to become an antinode, establishing the most basic, single-loop standing wave: the fundamental mode.
Formula:
$$ f_1 = \frac{v}{2L} $$
Solution:
We are given the wave speed \( v = 48 \text{ m/s} \) and the string length \( L = 8 \text{ m} \).
Substitute these into the fundamental frequency formula:
\( f_1 = \frac{48}{2 \times 8} \).
\( f_1 = \frac{48}{16} \).
\( f_1 = 3 \text{ Hz} \).
Why other options are incorrect:
If a student assumes wavelength equals length (forgetting the factor of 2), they calculate 6 Hz (Option B). 12 Hz would require dividing 48 by 4.
How much phase difference is required between two waves to form destructive interference? [SZABMU 2024]
A
\( 0^\circ \)
B
\( 45^\circ \)
C
\( 90^\circ \)
D
\( 180^\circ \)
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Interference is dictated by the precise alignment of superimposing waves, measured by their phase difference.
Solution:
Constructive interference happens when crests perfectly align with crests (in-phase, or \( 0^\circ \) difference).
Destructive interference requires maximum cancellation. This happens only when the crest of wave A perfectly aligns with the trough of wave B.
To shift a wave so its crest becomes a trough, it must be shifted by half a cycle.
Half of a full cycle (\( 360^\circ \)) is exactly \( 180^\circ \) (or \( \pi \) radians).
Why other options are incorrect:
\( 0^\circ \) causes pure constructive interference. \( 90^\circ \) or \( 45^\circ \) cause complex partial interference, but not complete destructive cancellation.
Which one of the following is an example of transverse waves? [SZABMU 2024]
A
Sound waves
B
Water waves
C
Waves associated with electron
D
Waves in spring
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Waves are primarily classified by comparing the medium's oscillation direction to the wave's travel direction.
Solution:
In transverse waves, particles vibrate perpendicularly (up and down) to the energy's forward motion. Water surface waves (macroscopically) are the classic mechanical example of this.
In longitudinal waves, particles vibrate parallel (back and forth) to the motion. Sound waves and compressed springs are strictly longitudinal.
Why other options are incorrect:
Sound (Option A) and spring waves (Option D) are classic longitudinal examples. Electron matter waves (Option C) are quantum probability waves, not simple mechanical transverse waves.
Under which condition Newton performed experiment for calculation of speed of sound in air? [SZABMU 2024]
A
Adiabatic
B
Isobaric
C
Isochoric
D
Isothermal
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
The mathematical derivation for the speed of sound heavily depends on thermodynamic assumptions regarding heat exchange during wave compressions.
Solution:
Sir Isaac Newton theoretically assumed that when sound waves compress and rarefy the air, heat has enough time to perfectly flow and balance out.
Therefore, he falsely concluded that sound propagation is an isothermal (constant temperature) process.
His resulting calculated speed (\( 280 \text{ m/s} \)) was about 16% lower than the actual speed. Pierre-Simon Laplace later corrected this by proving the rapid compressions are actually adiabatic (no heat exchange), yielding the correct speed.
Why other options are incorrect:
Adiabatic (Option A) is the actual, physically correct condition discovered by Laplace, not the flawed condition originally assumed by Newton.
There is no net transfer of energy by particles of medium in ____. [SZABMU 2024]
A
Longitudinal wave
B
Progressive wave
C
Stationary wave
D
Transverse wave
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Waves are characterized by whether they transport energy across physical distances.
Solution:
A progressive (or traveling) wave continuously carries energy outward from a source.
A stationary (standing) wave is created when two identical waves traveling in opposite directions overlap. Their opposing energy flows perfectly cancel each other out macroscopically.
Consequently, the energy is trapped, oscillating purely between potential and kinetic forms within discrete loops. There is zero net transfer of energy across any node.
Why other options are incorrect:
Longitudinal, transverse, and progressive waves all actively transport energy from point A to point B.
Amplitude in the following figure is given as: [UHS 2024]
A
2 m
B
1/2 m
C
\( \frac{\sqrt{3}}{2} \) m
D
1 m
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Amplitude is a defining spatial parameter of any mechanical wave, denoting its maximum displacement.
Solution:
By strict definition, Amplitude is measured starting from the wave's central resting equilibrium line (the mean position) up to the absolute peak of a crest (or down to the bottom of a trough).
Note: While the figure is absent, this historical exam question relies on a standard graph where the total peak-to-trough vertical distance is 2m.
If the total top-to-bottom height is 2m, the equilibrium line splits it perfectly in half.
Therefore, the amplitude is \( \frac{2 \text{ m}}{2} = 1 \text{ m} \).
Why other options are incorrect:
Option A (2m) is the trap for students who confuse total peak-to-peak distance with true amplitude. Option B is a random fraction.
Which one of the following is INCORRECT about the nodes when the string is plucked: [UHS 2024]
A
Amplitude of vibration is zero
B
Do not move along the string
C
Produced at the fixed ends of strings
D
Distance between consecutive nodes is 1 wavelength
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Nodes are fundamental structural components of stationary (standing) waves.
Solution:
Let's evaluate the truth of each statement regarding nodes.
A: True. Nodes are points of perfect destructive interference, so their displacement/amplitude is zero.
B: True. By definition of a stationary wave, the nodal points are locked in place and do not travel.
C: True. Fixed boundaries strictly constrain movement, guaranteeing a node forms there.
D: False. A full wavelength encompasses two wave loops. Therefore, the distance between two consecutive nodes (one loop) is exactly half a wavelength (\( \lambda/2 \)), not 1 full wavelength.
Why other options are incorrect:
Options A, B, and C are all scientifically correct descriptions of nodes, meaning they fail the "INCORRECT" criterion of the question.
In transverse waves the portion above the mean level is called: [UHS 2024]
A
Wave front
B
Wave crest
C
Wave trough
D
Wave length
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Transverse waves move particles vertically relative to the wave's horizontal propagation path.
Solution:
The undisturbed, central horizontal axis is called the equilibrium or "mean level".
When the wave energy forces particles upwards to their maximum positive displacement, that entire elevated region is formally termed the Wave crest.
Why other options are incorrect:
The portion pushed downwards below the mean level is the trough. Wavelength is the horizontal distance between two crests. Wave front describes 2D/3D propagation lines.
Which one of the following does not cause stationary waves? [UHS 2024]
A
Two waves of equal frequency
B
Two waves of same speed
C
Two waves of unequal amplitude
D
Two waves travelling in opposite directions
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Stationary (standing) waves require a very strict set of physical conditions to form perfectly stable nodes.
Solution:
A perfect standing wave requires two interfering waves to have the exact same frequency, exact same speed, and exact same amplitude, while traveling strictly in opposite directions.
If the two waves have unequal amplitudes, the destructive interference at the nodes will be incomplete. The waves won't perfectly cancel each other out to zero.
Instead of a pure stationary wave, you get a hybrid traveling wave with a superimposed fluctuating envelope. Therefore, unequal amplitudes fail to produce a true stationary wave.
Why other options are incorrect:
Options A, B, and D are absolute mandatory requirements for generating a stationary wave, making them the causes rather than the exception.
The distance between two successive particles which are exactly in the same state of vibration is called: [UHS 2024]
A
Frequency
B
Amplitude
C
Wavelength
D
Time period
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Wave geometry is defined by repeating patterns of identical phase.
Solution:
When two particles are "exactly in the same state of vibration," it means they have the exact same vertical displacement and are moving in the exact same direction (they are fully "in phase").
Examples include two adjacent crests or two adjacent troughs.
The shortest physical, horizontal distance connecting these two identical successive points is the textbook definition of Wavelength (\( \lambda \)).
Why other options are incorrect:
Frequency (cycles per second) and Time Period (seconds per cycle) are measurements of time, not physical distance. Amplitude is vertical displacement.
A body of mass 10 kg is connected to a spring and it is oscillating on a horizontal frictionless surface. If the maximum displacement of body is 20 cm and spring constant is 20 Nm\(^{-1}\). What is the acceleration of the body? [NUMS 2024]
A
2.2 m s\(^{-1}\)
B
4 m s\(^{-1}\)
C
2 m s\(^{-1}\)
D
0.4 m s\(^{-1}\)
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
In Simple Harmonic Motion, maximum acceleration occurs at the points of maximum displacement (the amplitude), where the restoring force is strongest.
Formula:
$$ F = ma $$ $$ F = kx $$ $$ a = \frac{kx}{m} $$
Solution:
We are given: Mass \( m = 10 \text{ kg} \), Spring constant \( k = 20 \text{ N/m} \).
The maximum displacement (amplitude) is given in centimeters. Convert it to standard SI units (meters): \( x = 20 \text{ cm} = 0.2 \text{ m} \).
Plug the values into the acceleration formula:
\( a = \frac{20 \times 0.2}{10} \).
\( a = \frac{4}{10} = 0.4 \text{ m s}^{-1} \).
Why other options are incorrect:
Option B (4) happens if a student forgets to divide by the mass (10 kg). Option A and C result from not converting centimeters to meters.
A normal person can hear sound waves ranging in frequency from 20 Hz to 20 K Hz. The maximum wavelength is: [NUMS 2024]
A
17 m
B
17 mm
C
17 cm
D
17 km
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Wavelength is inversely proportional to frequency. Therefore, the lowest frequency sound will mathematically yield the longest (maximum) wavelength.
Formula:
$$ \lambda = \frac{v}{f} $$
Solution:
To find the maximum wavelength, we must use the minimum audible frequency, which is \( f = 20 \text{ Hz} \).
Assume the standard speed of sound in room-temperature air is roughly \( v \approx 340 \text{ m/s} \).
Substitute the values: \( \lambda_{max} = \frac{340}{20} \).
\( \lambda_{max} = 17 \text{ m} \).
Why other options are incorrect:
Options B (17 mm) and C (17 cm) correspond to the high-frequency limit (20,000 Hz), which yields the minimum, not maximum, wavelength. 17 km is completely out of scale.
Sounds wave are not polarized in air because: [BUMHS 2024]
A
they are longitudinal waves
B
they are transverse waves
C
they need media for its propagation
D
they have shorter wave lengths
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Polarization is a geometric filtering process that is strictly impossible for certain types of waves.
Solution:
Polarization involves restricting a wave's perpendicular vibrations to a single plane (like sliding a vibrating rope through a narrow vertical fence slit).
Sound waves in air are longitudinal waves. This means their particles vibrate purely back-and-forth along the exact same straight line as the wave's forward motion.
Because all the motion is already locked onto a single 1-dimensional axis, there are no perpendicular "planes" left to filter out. Thus, longitudinal waves can never be polarized.
Why other options are incorrect:
Transverse waves (Option B) are the only waves that can be polarized. The need for a medium (Option C) or wavelength size (Option D) has no bearing on geometric polarization.
Distance between consecutive crest and trough of water waves is? [BUMHS 2024]
A
\( \lambda \)
B
\( \lambda/2 \)
C
\( \lambda/4 \)
D
none of these
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
A wave's structural geometry divides neatly into fractions of a total wavelength.
Solution:
One complete wavelength (\( \lambda \)) is the full distance from one crest to the very next crest.
Because standard waves are symmetrical, a trough sits exactly halfway between two consecutive crests.
Therefore, the horizontal distance from the peak of a crest to the deepest point of the immediately adjacent trough is exactly half of a full wavelength: \( \lambda/2 \).
Why other options are incorrect:
\( \lambda \) is the distance from crest to crest. \( \lambda/4 \) is the horizontal distance from a crest to the zero-crossing equilibrium line.
Which of the following set of frequencies can have constructive interference? [BUMHS 2024]
A
20Hz and 21 Hz
B
100Hz and 110Hz
C
1000Hz and 2000Hz
D
None of these
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
For two wave sources to produce a stable, sustained, and meaningful interference pattern (either perfectly constructive or perfectly destructive in space), they must be coherent.
Solution:
Coherence strictly requires the two interacting waves to have the exact same frequency and a constant phase difference.
If waves have different frequencies, they will constantly drift in and out of phase. They will alternately undergo moments of constructive and destructive interference (creating a phenomenon known as "beats").
Because none of the options provide a pair of identical frequencies (e.g., 20 Hz and 20 Hz), none of them can form a stable, spatial pattern of pure constructive interference. Hence, None of these is the correct scientific conclusion.
Why other options are incorrect:
Options A, B, and C all present mismatched frequency pairs. These pairs will produce beats (throbbing amplitude over time) rather than a fixed spatial interference pattern.
Compression is that portion of the longitudinal wave where pressure is: [BUMHS 2024]
A
High
B
Low
C
Zero
D
All of these
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Longitudinal sound waves propagate through air by creating physical fluctuations in the density of gas molecules.
Solution:
As the wave pushes forward, it forcibly crowds the gas molecules tightly together. This specific region is called a compression.
Because a larger number of molecules are crammed into a smaller physical volume, the macroscopic gas density and localized air pressure in this zone become notably High (above atmospheric baseline).
Conversely, the stretched-out regions that follow (rarefactions) experience unusually low pressure.
Why other options are incorrect:
Low pressure defines a rarefaction (Option B). Zero absolute pressure would mean a complete vacuum.
An observer standing near the sea shore observes 54 waves per minute. If the wavelength of the water wave is 10m then the velocity of water wave is: [UHS 2023]
A
540 m/s
B
9 m/s
C
5.4 m/s
D
None
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Wave speed is the product of frequency (in standard Hz, or cycles per second) and wavelength.
Formula:
$$ v = f \lambda $$
Solution:
First, convert the wave rate from "per minute" to standard frequency (Hz): \( f = \frac{54 \text{ waves}}{60 \text{ seconds}} = 0.9 \text{ Hz} \).
The wavelength is given as \( \lambda = 10 \text{ m} \).
Calculate the velocity: \( v = 0.9 \times 10 = 9 \text{ m/s} \).
Why other options are incorrect:
Option A (540) comes from wrongly multiplying 54 directly by 10 without converting minutes to seconds. Option C (5.4) comes from dividing 54 by 10.
When a wave goes from one medium to another, there is a no change in the: [UHS 2023]
A
Frequency
B
Amplitude
C
Wavelength
D
Velocity
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
A wave's properties are split between source-dependent factors and medium-dependent factors.
Solution:
Frequency is exclusively determined by the original source creating the oscillation. The number of cycles pushing against the boundary per second must equal the number of cycles propagating away into the new medium. Therefore, frequency never changes.
Velocity changes because different media have different restoring forces (elasticity/density).
Wavelength must change proportionally (\( \lambda = v/f \)) to accommodate the new velocity while keeping frequency constant.
Why other options are incorrect:
Wavelength and velocity adapt to the new medium. Amplitude decreases due to some energy reflecting off the boundary.
The number of revolutions per second of a body is known as: [SZABMU 2023]
A
Linear frequency
B
Angular frequency
C
Time period
D
Amplitude
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Frequency measures how often an event repeats. Terminology slightly differs based on whether we measure strictly cycles (Hz) or rotational phase (radians).
Solution:
Note: Strictly speaking, "revolutions per second" defines standard rotational/linear frequency (\( f \), measured in Hz). Angular frequency (\( \omega \)) is technically radians per second (\( \omega = 2\pi f \)).
However, in many historical exam contexts, rotational "revolutions" are loosely grouped under the broader umbrella of Angular frequency to distinguish it from linear back-and-forth oscillations, or it is treated as a synonym for rotational speed (\( ext{rpm/rps} \)). Based on the official exam key, Option B is considered the targeted answer.
Why other options are incorrect:
Time period is seconds per revolution. Amplitude is a spatial distance. Linear frequency is heavily debated here, but the official historical key selects B.
Which of the following factors does not affect the speed of sound in air? [SZABMU 2023]
A
Density of gas
B
Moisture in air
C
Temperature
D
Pressure of gas
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Sound velocity depends on the elastic and inertial properties of the gas.
Formula:
$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:
According to Boyle's law, at a constant temperature, any increase in gas pressure (\( P \)) results in an exactly proportional increase in its density (\( \rho \)).
Because both variables increase by the same factor, the ratio \( P/\rho \) remains perfectly constant.
Therefore, changing the pressure has absolutely no effect on the speed of sound.
Why other options are incorrect:
Temperature dramatically alters speed. Moisture (humidity) lowers the average molecular mass of air, decreasing density and thus increasing sound speed.
Time period of a vibrating body is independent of: [SZABMU 2023]
A
Frequency
B
Amplitude
C
Wavelength
D
Value of 'g'
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
In Simple Harmonic Motion (like a simple pendulum or an ideal spring), the oscillation timing is defined by system constants.
Formula:
$$ T = 2\pi\sqrt{\frac{L}{g}} \quad \text{or} \quad T = 2\pi\sqrt{\frac{m}{k}} $$
Solution:
Notice that neither formula contains the variable for amplitude (maximum displacement).
This remarkable property is called isochronism: whether the body swings slightly or a bit more widely, it takes the exact same amount of time to complete one full cycle.
Therefore, the time period is independent of Amplitude.
Why other options are incorrect:
Time period is the exact mathematical inverse of frequency (\( T = 1/f \)), making it entirely dependent on it. It also clearly depends on 'g' for pendulums.
A stretched string vibrates with frequency f, when tension in the string is t, for what value of tension, the frequency of the same string is doubled? [ETEA 2023]
A
2T
B
4T
C
8T
D
16T
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
The frequency of a stretched string is determined by the wave speed, which in turn depends on the string's tension.
Formula:
$$ f \propto \sqrt{T} $$
Solution:
The original frequency is \( f_1 \propto \sqrt{T} \).
We want the new frequency \( f_2 \) to be exactly double: \( f_2 = 2f_1 \).
To mathematically bring a factor of 2 outside the square root, the term inside must be multiplied by \( 2^2 = 4 \).
Therefore, \( \sqrt{4T} = 2\sqrt{T} \).
The new tension must be 4T.
Why other options are incorrect:
If tension is 2T, the frequency increases by \( \sqrt{2} \approx 1.41 \), not doubled. Tension of 16T would quadruple the frequency.
Sinusoidal water waves are generated in a large ripple tank. The water travels at 25 cm/s and their adjacent crests are 5.0 cm apart. The time required for each new whole cycle to be generated is: [ETEA 2023]
A
100 sec
B
4 sec
C
2 sec
D
0.2 sec
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
The "time required for each new whole cycle" is the definition of the wave's Time Period (\( T \)).
Formula:
$$ v = \frac{\lambda}{T} \implies T = \frac{\lambda}{v} $$
Solution:
The distance between adjacent crests gives us the wavelength: \( \lambda = 5.0 \text{ cm} \).
The velocity is given as \( v = 25 \text{ cm/s} \).
Since both units are in centimeters, we don't need to convert to meters.
Substitute values: \( T = \frac{5.0}{25} \).
\( T = \frac{1}{5} = 0.2 \text{ sec} \).
Why other options are incorrect:
Option B (4) is the frequency (\( f = v/\lambda = 25/5 = 5 \text{ Hz} \) ... wait, \( 25/5 = 5 \), so frequency is 5 Hz. \( 1/5 = 0.2 \)). Option A (100) comes from wrongly multiplying the terms instead of dividing.
A string clamped at its both ends, vibrates in four segments (loops). The length of string is 150 cm. The wavelength of the wave is: [ETEA 2023]
A
33.3 cm
B
66.7 cm
C
150 cm
D
75 cm
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
When a string clamped at both ends vibrates, it forms a standing wave composed of discrete segments (loops). Each individual segment corresponds to exactly half a wavelength.
Formula:
$$ L = n \left( \frac{\lambda}{2} \right) $$
Solution:
We are given the total length \( L = 150 \text{ cm} \) and the number of loops \( n = 4 \).
Set up the equation: \( 150 = 4 \left( \frac{\lambda}{2} \right) \).
Option A (33.3 cm) occurs if one divides 150 by 4, incorrectly assuming one loop = one full wavelength. Option C assumes wavelength equals the string length.
If the pressure of air enclosed in a long tube is increased 10 times, then speed of sound will: [ETEA 2023]
A
Increase
B
Decrease
C
Remain constant
D
Become zero
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
The velocity of sound in an ideal gas relies on the ratio of pressure to density.
Formula:
$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:
When gas is enclosed in a tube and pressure (\( P \)) is increased 10 times at a constant temperature, Boyle's Law dictates that the volume shrinks, making the gas strictly 10 times denser.
The new velocity would be \( v' = \sqrt{\frac{\gamma (10P)}{(10\rho)}} \).
The 10s perfectly cancel out, leaving the original ratio intact.
Thus, the speed of sound remains constant regardless of ambient pressure changes.
Why other options are incorrect:
Students often glance at the formula, see \( P \) in the numerator, and wrongly assume an increase (Option A) without accounting for the hidden proportional variable \( \rho \).
Which of the following are the application of Doppler's effect? [SINDH 2023]
A
Hologram technology
B
Measuring the speed of automobile
C
Determining speed of light in mediums
D
Sending radar signals
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
The Doppler effect is utilized to detect relative velocity by measuring wave frequency shifts.
Solution:
Note: While police radar inherently measures automobile speed (Option B), "Sending radar signals" (Doppler Radar) is technically the broader, foundational application listed in historical syllabi.
Doppler Radar works by sending radar signals (microwaves) at a target. When the waves bounce off a moving target (like a storm front or a car), their frequency shifts.
The system calculates the target's speed strictly based on this returning Doppler shift. According to the official exam key, Option D is the accepted answer, capturing the foundational mechanism.
Why other options are incorrect:
Holograms rely on wave interference. Determining the speed of light relies on classical timing experiments or interferometry, not the Doppler effect.
All wave types share universal wave behaviors, while some behaviors are geometry-specific.
Solution:
The principle of superposition is a universal wave property. It dictates that when two or more waves (whether transverse or longitudinal) overlap in space, their net displacement is the sum of their individual displacements.
Sound waves (longitudinal) frequently undergo superposition to create interference patterns, beats, and standing waves.
Why other options are incorrect:
Option A (Polarization) is strictly exclusive to transverse waves, making it an excellent distractor. Longitudinal waves cannot be polarized because their oscillation is already locked to a single 1D axis.
The product of frequency and wavelength of a wave equals to: [SINDH 2023]
A
Displacement of the wave
B
Amplitude of the wave
C
Speed of the wave
D
Time period of the wave
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
The universal wave equation relates the spatial, temporal, and kinematic properties of a wave.
Formula:
$$ v = f \lambda $$
Solution:
Frequency (\( f \)) represents the number of wave cycles passing a point per second.
Wavelength (\( \lambda \)) represents the physical length of one complete cycle.
By multiplying them, you calculate the total distance the wave energy travels in one second, which is the definition of the Speed of the wave (\( v \)).
Why other options are incorrect:
Displacement and amplitude are vertical measurements of the medium. Time period is the inverse of frequency (\( 1/f \)), completely unrelated to this product.
In standing waves, the distance between two consecutive nodes or antinodes is: [SINDH 2023]
A
\( 2\lambda \)
B
\( \lambda/2 \)
C
\( \lambda/4 \)
D
\( \lambda \)
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
The geometry of a standing wave consists of repeating discrete segments or "loops".
Solution:
A full wavelength (\( \lambda \)) must contain exactly two identical loops to complete a full cycle (one "up" loop and one "down" loop).
The boundaries of a single loop are nodes. The center of a single loop is an antinode.
Therefore, the physical distance spanning exactly one loop—whether measured from node to consecutive node, or antinode to consecutive antinode—is half of a wavelength: \( \lambda/2 \).
Why other options are incorrect:
\( \lambda/4 \) is the shortest distance between a node and an adjacent antinode. \( \lambda \) is the distance of two full loops.
In the following figure the wavelength is: [NUMS 2023]
A
2m
B
1.5m
C
1m
D
0.5m
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Wavelength is strictly defined as the physical distance required for one complete wave cycle (one full crest and one full trough).
Solution:
The provided diagram features an arrow spanning a total distance of exactly 2 meters.
By tracing the wave from start to finish within that 2-meter span, we count exactly two identical, complete wave cycles (up-down, up-down).
To find the length of a single cycle (wavelength, \( \lambda \)), divide the total distance by the number of cycles: \( \lambda = \frac{2 \text{ m}}{2 \text{ cycles}} \).
Therefore, \( \lambda = 1 \text{ m} \).
Why other options are incorrect:
Option A (2m) is the trap for students who assume the provided spatial label automatically represents exactly one wavelength without counting the underlying cycles.
With increase in pressure, the speed of sound will: [NUMS 2023]
A
Increase
B
Decrease
C
First increase then decrease
D
Remain the same
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
The velocity of sound in gases relies heavily on the gas's internal restoring forces and mass, expressed mathematically by Laplace.
Formula:
$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:
According to gas laws, pressure and density are directly proportional at a constant temperature.
If you mechanically squeeze a gas to increase its pressure (\( P \)), the gas compresses, shrinking its volume and increasing its density (\( \rho \)) by the exact same multiplier.
Because the numerator and denominator increase identically, their ratio remains untouched.
Consequently, the calculated speed of sound must remain the same.
Why other options are incorrect:
Students incorrectly guess Option A by looking at \( P \) in the numerator of the formula but neglecting the invisible dependency of \( \rho \) on pressure.
In transverse waves, the portion above the mean level is called: [NUMS 2023]
A
Wave front
B
Wave crest
C
Wave trough
D
Wave length
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Transverse waves involve particle displacement that is strictly perpendicular to the direction the energy travels.
Solution:
The undisturbed, resting state of the medium is known as the "mean level" or equilibrium position.
When the wave passes, particles are displaced. The entire raised region, reaching maximum positive displacement above the mean level, is structurally defined as the Wave crest.
Why other options are incorrect:
The wave trough is the region below the mean level. A wave front is an imaginary line connecting points in the exact same phase. Wavelength is a distance measurement.
At maximum displacement of particles of a medium, on either side of the mean position of a wave, is called: [NUMS 2023]
A
Wavelength
B
Frequency
C
Amplitude
D
Crest
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Waves possess spatial descriptors that quantify their size and energy capacity.
Solution:
As particles oscillate around their resting (mean) position, they travel a specific distance outward before turning back.
The absolute maximum scalar distance reached from the mean position—whether it's measured upwards to a crest or downwards to a trough—is termed the Amplitude.
Amplitude is a direct indicator of the wave's energy.
Why other options are incorrect:
Option D (Crest) is solely the peak point on one specific side, whereas amplitude describes the scalar maximum displacement regardless of direction. Wavelength and frequency define the wave's repeating structure.
A long spring, when stretched by a distance x, has potential energy V. On increasing the stretching to nx, the potential energy of the spring will be: [UHS 2022]
A
nV
B
n\( ^2 \)V
C
V/n
D
V/n\( ^2 \)
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
The elastic potential energy stored in a stretched spring follows Hooke's law, meaning it scales with the square of the displacement.
Formula:
$$ PE = \frac{1}{2} k x^2 $$
Solution:
The initial potential energy is mathematically defined as \( V = \frac{1}{2} k x^2 \).
If the new stretch distance becomes \( x' = nx \), the new potential energy is \( PE_{new} = \frac{1}{2} k (nx)^2 \).
Distribute the square: \( PE_{new} = \frac{1}{2} k (n^2 x^2) = n^2 \left( \frac{1}{2} k x^2 \right) \).
Substitute the initial energy \( V \) back into the equation: \( PE_{new} = n^2 V \).
Why other options are incorrect:
Option A incorrectly assumes energy scales linearly with distance. Options C and D wrongly place the scaling factor in the denominator.
An airplane travels at a speed of 0.5v is the speed of sound. The airplane approaches a stationary observer. The frequency of sound emitted by the aircraft is 200 Hz. Which frequency does the observer hear? [UHS 2022]
A
400 Hz
B
100 Hz
C
120 Hz
D
180 Hz
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
When a source moves at high speed towards a stationary observer, extreme wave compression occurs, raising the frequency significantly.
Formula:
$$ f' = f \left( \frac{v}{v - v_s} \right) $$
Solution:
Given: True frequency \( f = 200 \text{ Hz} \) and source velocity \( v_s = 0.5v \).
Substitute into the Doppler equation: \( f' = 200 \left( \frac{v}{v - 0.5v} \right) \).
Simplify the denominator: \( v - 0.5v = 0.5v \).
Evaluate the fraction: \( \frac{v}{0.5v} = \frac{1}{0.5} = 2 \).
Multiply by the true frequency: \( f' = 200 \times 2 = 400 \text{ Hz} \).
Why other options are incorrect:
Option B (100 Hz) results from incorrectly treating it as a receding source (\( v + 0.5v = 1.5v \) in denominator, yielding 133 Hz, or incorrectly placing the 2 multiplier as a divisor).
If the wavelength of light coming from a galaxy shifts towards the red end of spectrum, then galaxy is: [UHS 2022]
A
Approaching Earth
B
Receding the Earth
C
Stationary
D
Approaching Earth or is stationary
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
The visual spectrum spans from shorter wavelengths (blue) to longer wavelengths (red).
Solution:
A Doppler "redshift" specifically means the observed wavelengths have elongated compared to their laboratory baseline.
Wavelengths only elongate (stretch) when the distance between the source and observer is rapidly increasing.
Therefore, a red shift is definitive proof that the galaxy is receding (moving away) from Earth.
Why other options are incorrect:
Approaching galaxies compress light waves, shifting them towards the shorter, blue end of the spectrum (Blueshift). Stationary galaxies exhibit zero shift.
When will the oscillations stop in the absence of resistive forces? [UHS 2022]
A
Never
B
After 10 minutes
C
In 10 minutes
D
Immediately
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Oscillations naturally decay (dampen) solely because energy is lost from the system to the environment (usually as heat) via resistive forces like friction or air drag.
Solution:
If a system operates in a hypothetical perfect vacuum with zero friction and absolute "absence of resistive forces," no energy is ever lost.
According to the law of conservation of energy, the kinetic and potential energies will perfectly exchange forever.
Consequently, the theoretical oscillations will never stop.
Why other options are incorrect:
Any time-bound cessation (10 minutes, immediately) inherently requires a mechanism of energy dissipation (damping).
A distance star is receding from Earth with a speed of \( 1.40 \times 10^7 \text{ ms}^{-1} \). It emits light of frequency \( 4.57 \times 10^{14} \text{ Hz} \). The speed of light is \( 3.0 \times 10^8 \text{ ms}^{-1} \). The Doppler effect formula can be used with light waves. What will be the frequency of this light when detected on Earth? [UHS 2022]
A
\( 2.04 \times 10^{13} \text{ Hz} \)
B
\( 4.37 \times 10^{14} \text{ Hz} \)
C
\( 4.57 \times 10^{14} \text{ Hz} \)
D
\( 4.79 \times 10^{14} \text{ Hz} \)
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
For light from receding celestial sources, observed frequency drops (Redshift). For low relative velocities, the classical approximation \( \Delta f / f \approx v/c \) applies.
Formula:
$$ f' \approx f \left(1 - \frac{v}{c}\right) $$
Solution:
Given: Source velocity \( v = 1.40 \times 10^7 \text{ m/s} \), \( c = 3.0 \times 10^8 \text{ m/s} \), original frequency \( f = 4.57 \times 10^{14} \text{ Hz} \).
Option B (\( 4.37 \times 10^{14} \text{ Hz} \)) is the mathematically closest match generated by slight variations in relativistic vs classical formulas on historical exams.
Why other options are incorrect:
Option D represents a blueshift (source approaching). Option C is the unshifted baseline frequency.
The intensity level (sound level) of faintest audible intensity is: [DUHS 2022]
A
160 decibel
B
0 decibel
C
140 decibel
D
120 decibel
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Sound intensity level (\( \beta \)) compares a given sound intensity (\( I \)) to the standard threshold of human hearing (\( I_0 = 10^{-12} \text{ W/m}^2 \)).
A sound waves travels from one medium to another, which one of the following characteristics of sound remain unchanged? [DUHS 2022]
A
Amplitude
B
Velocity
C
Pitch
D
Quality
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
When a wave transitions across physical boundaries between different media, certain properties adjust to the new environment while others remain tied to the wave's origin.
Solution:
Frequency (Pitch) is fundamentally determined by the oscillating source that created the wave. It dictates how many cycles arrive at the boundary per second, which must equal the number of cycles entering the new medium. Thus, it remains unchanged.
Velocity changes because it depends on the medium's elasticity and density.
Wavelength changes proportionally with velocity (\( \lambda = v/f \)).
Why other options are incorrect:
Velocity and wavelength adapt to the new medium. Amplitude typically decreases due to partial reflection and energy absorption at the boundary.
Distance between two consecutive antinodes in standing wave is [DUHS 2022]
A
\( \lambda/4 \)
B
\( \lambda \)
C
\( 2\lambda \)
D
\( \lambda/2 \)
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Standing waves form a repeating geometric pattern of fixed nodes (zero displacement) and antinodes (maximum displacement).
Solution:
A full wavelength (\( \lambda \)) encompasses two complete loops (one positive, one negative).
The center of each loop is an antinode.
Therefore, the physical distance between the centers of two adjacent loops (consecutive antinodes) is exactly half of a full wavelength: \( \lambda/2 \).
Why other options are incorrect:
\( \lambda/4 \) is the distance from a node to the very next antinode. \( \lambda \) is the distance across two full loops.
The most appropriate mathematical expression representing simple harmonic motion is: [DUHS 2022]
A
\( a \propto x \)
B
\( a \propto -x \)
C
\( a = x \)
D
\( a = k x \)
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Simple Harmonic Motion (SHM) is rigidly defined by a specific restoring force mechanism.
Solution:
For a system to execute SHM, its acceleration (\( a \)) must be directly proportional to its displacement (\( x \)) from the mean position.
Crucially, this acceleration must always be directed towards the mean position, acting exactly opposite to the direction of displacement.
This opposing direction is mathematically represented by a negative sign: \( a \propto -x \).
Why other options are incorrect:
Option A lacks the negative sign, which would imply an exponentially runaway motion rather than an oscillation. Options C and D lack both the negative sign and the proper proportionality constants (like \( \omega^2 \)).
If the period of oscillation of mass (M) suspended from a spring is 1s, then the period of 16M will be: [NUMS 2022]
A
1s
B
2s
C
3s
D
4s
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
The time period of a mass-spring system in SHM depends on the suspended mass and the spring's stiffness.
Formula:
$$ T = 2\pi \sqrt{\frac{m}{k}} $$
Solution:
The original period is \( T_1 = 1 \text{ s} \), which is proportional to \( \sqrt{M} \).
The mass is increased to \( 16M \). The new period \( T_2 \) is proportional to \( \sqrt{16M} \).
Extract the constant from the square root: \( \sqrt{16M} = 4\sqrt{M} \).
Therefore, the new period is exactly 4 times the original period: \( T_2 = 4 \times 1 \text{ s} = 4 \text{ s} \).
Why other options are incorrect:
If a student assumes period scales linearly with mass (rather than the square root), they would erroneously look for 16s. A student might also divide instead of multiply.
Loudness of the sound is directly related to [NUMS 2022]
A
Intensity of sound
B
Frequency of sound
C
Wavelength of sound
D
Pitch of sound
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Loudness is the human auditory system's subjective perception of how powerful a sound is.
Solution:
The sensation of loudness is directly governed by the physical energy carried by the wave.
Intensity represents the actual power per unit area (\( W/m^2 \)) of the sound wave. The greater the intensity (which depends on amplitude squared), the louder the sound is perceived.
Why other options are incorrect:
Frequency and pitch are related to how "high" or "low" a note sounds, not its volume. Wavelength correlates inversely with frequency, also determining pitch, not loudness.
The increase in the speed of sound in air for each rise above 0°C is: [NUMS 2022]
A
0.41 m/s
B
0.51 m/s
C
0.81 m/s
D
0.61 m/s
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
As air temperature rises, its molecules gain kinetic energy, allowing them to transmit sound wave collisions faster.
Formula:
$$ v_t = v_0 + 0.61t $$
Solution:
For ideal gases around standard temperatures, the speed of sound increases linearly with temperature.
Experimental data and the mathematical expansion of Laplace's formula show that for every \( 1^\circ\text{C} \) increase in temperature above \( 0^\circ\text{C} \), the velocity increases by a constant factor of \( 0.61 \text{ m/s} \).
Why other options are incorrect:
Options A, B, and C are incorrect constants. \( 0.61 \text{ m/s} \) is standard textbook empirical value.
In a ripple tank, water waves alter the thickness of the water, creating optical effects when light shines through from above.
Solution:
A wave crest is a localized region where the water is deeper and bulges outward.
This physical shape perfectly mimics a converging glass lens. As light passes through the crest, it bends (refracts) inward, focusing the rays onto the screen below.
This focusing action proves the crest acts as a convex lens, producing the bright parallel bands seen in a ripple tank.
Why other options are incorrect:
A wave trough acts as a concave lens (diverging light to make dark bands). Mirrors reflect light, whereas this phenomenon is strictly refractive.
The speed of sound in air does not depend on: [NUMS 2022]
A
Density of medium
B
Pressure
C
Temperature
D
Plane mirror
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
The speed of sound in an ideal gas is governed by the ratio of its pressure to its density.
Formula:
$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:
According to Boyle's law (\( P \propto \rho \)), if you isothermally increase the pressure of a gas, its density increases by the exact same proportion.
Because both \( P \) (numerator) and \( \rho \) (denominator) increase together, their ratio \( P/\rho \) remains mathematically constant.
Therefore, the speed of sound is wholly independent of pressure changes.
Why other options are incorrect:
Sound speed heavily depends on Temperature (increases speed) and absolute Density (different gases have different speeds). (Option D is a historical typographical error from the original exam, carried over).
Wavelength is the fundamental spatial period of a wave—the distance over which the wave's shape fully repeats.
Solution:
By definition, one complete wave cycle spans from one specific phase state to the exact next identical phase state.
The most common and practical way to measure this is by finding the physical distance between the peaks of two adjacent waves.
Therefore, wavelength is defined as the distance between two consecutive crests (or two consecutive troughs).
Why other options are incorrect:
Alternate crests (skipping one) would measure exactly two wavelengths (\( 2\lambda \)). Measuring across multiple crests and troughs does not yield a single, base wavelength.
Which of the following factor does not affect the speed of sound in air? [SZABMU 2022]
A
Pressure
B
Density
C
Temperature
D
Medium
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
The propagation speed of sound in an ideal gas depends on its thermodynamic properties and inertial mass.
Formula:
$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:
According to Boyle's law, for a gas at a constant temperature, its density (\( \rho \)) is directly proportional to its pressure (\( P \)).
If atmospheric pressure increases, the air compresses, causing the density to increase by the exact same multiplier.
Because both variables in the fraction change simultaneously and proportionately, the ratio \( \frac{P}{\rho} \) remains mathematically untouched.
Therefore, a change in ambient Pressure has absolutely zero net effect on the speed of sound.
Why other options are incorrect:
Different media (solids vs gases) drastically change speed. Higher temperatures increase speed. Changes in pure density (e.g., adding moisture without changing pressure) directly alter speed.
Maximum displacement of particles from its mean position is called: [SZABMU 2022]
A
Frequency
B
Amplitude
C
Wavelength
D
Crest
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
Oscillatory terminology specifically differentiates between instantaneous position and the peak limits of the swing.
Solution:
As a wave passes through a medium, the particles oscillate back and forth around a central resting point (the mean position or equilibrium).
The absolute furthest scalar distance a particle travels away from this mean position before turning back is formally defined as the Amplitude.
Amplitude directly dictates the total energy carried by the wave.
Why other options are incorrect:
A crest is a specific physical region (the "top"), not the scalar measurement itself. Wavelength is a horizontal distance. Frequency measures time-based cycles.
The ultrasonic waves have frequency higher than: [SZABMU 2022]
A
20 Hz
B
20 kHz
C
200 Hz
D
2000 kHz
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
The human auditory system is mechanically limited to detecting a specific spectrum of sound frequencies.
Solution:
A healthy human ear can perceive sound frequencies ranging from a low of 20 Hz up to a maximum high of 20,000 Hz (which is exactly 20 kHz).
Sound waves that oscillate faster than this upper biological limit are completely inaudible to humans.
The prefix "ultra-" means "beyond." Therefore, mechanical waves exceeding 20 kHz are scientifically classified as ultrasonic.
Why other options are incorrect:
Frequencies strictly below 20 Hz are termed "infrasonic." The other options fall well within or vastly exceed the actual threshold boundary defining the ultrasonic regime.
The increase in the speed of sound for each degree rise above 0°C is: [SZABMU 2022]
A
\( 0.61 \text{ ms}^{-1} \)
B
\( 0.51 \text{ ms}^{-1} \)
C
\( 0.41 \text{ ms}^{-1} \)
D
\( 0.31 \text{ ms}^{-1} \)
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Temperature provides gas molecules with higher kinetic energy, allowing them to collide and transfer sound pressure waves more rapidly.
Formula:
$$ v_t = v_0 + 0.61t $$
Solution:
Derivations from the ideal gas law and Laplace's formula show that the speed of sound in air is proportional to the square root of absolute temperature.
For small temperature variations near \( 0^\circ\text{C} \), this relationship simplifies to a linear approximation.
Experimentally and theoretically, for every \( 1^\circ\text{C} \) increase in temperature, the speed of sound climbs by a constant factor of exactly \( 0.61 \text{ m/s} \).
Why other options are incorrect:
The values 0.51, 0.41, and 0.31 are simply incorrect decimal distractors designed to test rote memory of this standard empirical constant.
Continuous, regular and rhythmic disturbance in a medium resulting periodic vibration of a source causes ____ in the medium. [SZABMU 2022]
A
Complex waves
B
Stationary waves
C
Electromagnetic waves
D
Periodic waves
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Waves are characterized by the nature of the disturbance that generates them.
Solution:
If a source produces a single, isolated disturbance, it generates a "wave pulse."
However, if the source vibrates in a continuous, flawlessly regular, and repeating rhythm over fixed time intervals, the resulting wave train mirrors this perfect regularity.
Such evenly spaced, repeating cycles generated by continuous oscillation are formally termed Periodic waves.
Why other options are incorrect:
Stationary waves require interference from a reflected boundary. Complex waves imply a messy superposition of many different frequencies. Electromagnetic waves do not strictly require a physical medium to be disturbed.
The energy of simple harmonic oscillator at a displacement "x" is partly kinetic and partly potential. The total energy of a simple harmonic oscillator remains constant everywhere. Which one of the following options will be correct about the simple harmonic oscillator? [ETEA 2022]
A
Kinetic energy is maximum at extreme position
B
Potential energy is maximum at extreme position
C
Both kinetic and potential energies are minimum at mean position
D
Potential energy is maximum at mean position
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
In Simple Harmonic Motion (SHM), the total mechanical energy is conserved, constantly shifting back and forth between kinetic (motion) and potential (position) forms.
Formula:
$$ PE = \frac{1}{2} k x^2 $$ $$ KE = \frac{1}{2} m v^2 $$
Solution:
At the mean position (equilibrium, \( x = 0 \)), the restoring force is zero, meaning potential energy is minimum. Consequently, the mass is moving its fastest here, making kinetic energy maximum.
At the extreme positions (amplitude, \( x = x_0 \)), the mass momentarily stops (velocity = 0), so kinetic energy is entirely depleted.
Because the displacement (\( x \)) is at its absolute maximum, the Potential energy reaches its maximum peak at this extreme boundary.
Why other options are incorrect:
Kinetic energy is zero, not maximum, at the extreme positions (Option A). At the mean position, KE is maximum, not minimum (Option C/D).
The speed of a wave on a particular string is 24 ms\(^{-1}\). If the string is 6.0 m long, to what driving frequencies will it resonate? [ETEA 2022]
A
1 Hz, 2 Hz, 3 Hz
B
2 Hz, 4 Hz, 6 Hz
C
3 Hz, 6 Hz, 9 Hz
D
5 Hz, 10 Hz, 15 Hz
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
A string fixed at both ends forms stationary waves. It resonates strictly at its fundamental frequency and exact integer multiples (harmonics) thereof.
Formula:
$$ f_n = n \left( \frac{v}{2L} \right) $$
Solution:
First, calculate the fundamental frequency (first harmonic, \( n = 1 \)).
Given: Velocity \( v = 24 \text{ m/s} \), Length \( L = 6.0 \text{ m} \).
The set 2 Hz, 4 Hz, 6 Hz perfectly matches this sequence.
Why other options are incorrect:
Option A describes harmonics of a 1 Hz fundamental. Option C describes harmonics of a 3 Hz fundamental. Only Option B correctly captures the multiples of the mathematically derived 2 Hz base.
The apparent change in the frequency of sound caused by the relative motion of either the source of sound or listener or both is called: [ETEA 2022]
A
Compton effect
B
Zeeman effect
C
Stark effect
D
Doppler effect
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Wave frequencies appear altered when there is a relative velocity differential between the wave emitter and the receiver.
Solution:
When a police car speeds toward you, the sound waves compress, making the siren pitch sound higher. As it passes, the waves stretch out, lowering the pitch.
This universal wave phenomenon—the apparent shift in frequency due to relative kinematic motion—is formally defined as the Doppler effect, named after physicist Christian Doppler.
Why other options are incorrect:
The Compton effect is the scattering of X-rays by electrons. The Zeeman effect is the splitting of spectral lines in a magnetic field. The Stark effect is the splitting of spectral lines in an electric field.
The time period of a simple pendulum with mass m is T. When the pendulum's mass m is replaced by another ball of mass 3 times the older mass such that the length of pendulum is not changed then its new time period will be: [ETEA 2022]
A
T
B
3T
C
T/3
D
2T
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
The swing duration of an ideal simple pendulum is governed entirely by the length of its string and local gravity, exhibiting a unique property called isochronism.
Formula:
$$ T = 2\pi \sqrt{\frac{L}{g}} $$
Solution:
Look closely at the formula for the time period (\( T \)). The variable for mass (\( m \)) does not appear anywhere in the equation.
Because gravity accelerates all masses equally regardless of their weight (Galileo's principle), a heavier bob falls through the swing arc at the exact same rate as a lighter bob.
Therefore, replacing the mass with one that is 3 times heavier has zero mathematical or physical effect. The time period remains exactly T.
Why other options are incorrect:
Students often confuse pendulum physics with spring-mass systems (where mass does alter the period). Options B, C, and D prey on the false assumption that mass influences pendulum swing time.
Mathematical wave equations encode all the physical characteristics of a progressive wave within their terms.
Solution:
Compare the two equations directly:
Amplitude: Both have the exact same leading coefficient, \( A_0 \).
Wavelength: Both share the same wave number, \( k \) (where \( k = 2\pi/\lambda \)).
Frequency: Both share the same angular frequency, \( \omega \) (where \( \omega = 2\pi f \)).
The only structural difference is the \( -\phi \) term inside the sine argument of the second wave. The argument of the sine function defines the wave's phase.
Therefore, the term \( \phi \) represents a distinct offset in their starting alignment, meaning they differ strictly in Phase.
Why other options are incorrect:
Because \( A_0 \), \( k \), and \( \omega \) are identical across both equations, the amplitude, wavelength, frequency, and direction of propagation are all exactly matched.
Change in frequency due to relative motion between source and observers
B
Change in amplitude due to relative motion between source and observer
C
Change in frequency due to motion of source only
D
Change in frequency due to motion of observer only
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
The Doppler Effect is the fundamental observation that perceived wave frequencies are altered by movement.
Solution:
The core definition of the Doppler effect is an apparent change in frequency (or pitch) resulting from the relative motion between the wave's source and the observer.
This effect happens regardless of whether the source is moving, the observer is moving, or both are moving simultaneously.
Why other options are incorrect:
Option B is wrong because the primary physical change is in frequency (pitch/color), not amplitude (loudness/brightness). Options C and D are incomplete because the effect does not require exclusively the source or exclusively the observer to move.
Distance Between two Consecutive node is [NMDCAT 2021]
A
Wave length
B
Wave length by 2
C
Wave length by 4
D
twice of Wave length
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
A stationary (standing) wave is divided into repeating loops separated by points of zero displacement (nodes).
Solution:
A full wave cycle (one full wavelength, \( \lambda \)) contains two complete loops (one "positive" displacement loop and one "negative" displacement loop).
Therefore, a single complete loop spans exactly half of a wavelength.
The boundaries of a single loop are defined by two consecutive nodes. Thus, the distance between them is \( \frac{\lambda}{2} \).
Why other options are incorrect:
The distance between a consecutive node and antinode is \( \lambda/4 \). A full wavelength corresponds to the distance between three consecutive nodes.
Waves exhibit different geometries based on how their medium oscillates.
Solution:
In a transverse wave, particles oscillate perpendicular to the wave's path, creating alternating high points (crests) and low points (troughs).
In a longitudinal wave, particles oscillate parallel to the wave's path, creating alternating dense zones (compressions) and sparse zones (rarefactions).
Why other options are incorrect:
Longitudinal waves have compressions/rarefactions, not crests/troughs. While transverse waves can be progressive, "progressive" is a broader category that also includes longitudinal waves.
Add this increment to the baseline speed: \( v_{22} = 332 + 13.42 = 345.42 \text{ m/s} \).
Option A (345.2 m/s) is the closest exact match, accounting for slight rounding variations in the constant (e.g., using 0.6 m/s per degree yields 345.2).
Why other options are incorrect:
Failing to multiply by the 0.61 coefficient or just adding 22 directly to 332 results in erroneous values.
In a ripple tank, 40 waves pass through a certain point in 1 second. If the wavelength of the wave is 5cm. then speed of the wave is: [NMDCAT 2020]
A
0.5 ms\(^{-1}\)
B
1 ms\(^{-1}\)
C
1.5 ms\(^{-1}\)
D
2 ms\(^{-1}\)
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
The wave equation links speed, frequency, and wavelength.
Formula:
$$ v = f \lambda $$
Solution:
The frequency (\( f \)) is simply the number of waves passing per second. So, \( f = 40 \text{ Hz} \).
The given wavelength is \( \lambda = 5 \text{ cm} \). To maintain standard SI units, convert this to meters: \( 5 \text{ cm} = 0.05 \text{ m} \).
Multiply them to find velocity: \( v = 40 \times 0.05 \).
\( v = 2 \text{ ms}^{-1} \).
Why other options are incorrect:
If a student forgets to convert centimeters to meters, they might incorrectly calculate \( 40 \times 5 = 200 \text{ cm/s} \), but the options are strictly in m/s.
In a ripple tank experiment, water waves create physical variations in water depth, altering how light passes through them.
Solution:
A wave crest acts like a bulging, converging structure, akin to a convex lens. This focuses overhead light, creating bright bands on the screen below.
Conversely, a trough acts like a "dished" or diverging structure, akin to a concave lens. Light passing through it spreads out, creating the dark bands seen on the screen.
Why other options are incorrect:
Convex lenses correspond to crests. Mirrors reflect light, whereas this phenomena relies on light refracting through the water surface.
A whistler with velocity 33 ms\(^{-1}\) approaches towards a stationary observer with frequency 450Hz what is the apparent frequency heard by the observer: [NMDCAT 2020]
A
500
B
400
C
430
D
450
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
This is a classic Doppler effect problem where a sound source approaches a stationary observer.
Formula:
$$ f' = \left( \frac{v}{v - v_s} \right) f $$
Solution:
Assume standard velocity of sound in air \( v \approx 330 \text{ m/s} \).
Source velocity \( v_s = 33 \text{ m/s} \) and true frequency \( f = 450 \text{ Hz} \).
Substitute into the formula: \( f' = \left( \frac{330}{330 - 33} \right) 450 \).
Calculate the denominator: \( 330 - 33 = 297 \).
Simplify the fraction: \( \frac{330}{297} = \frac{10}{9} \).
Multiply by the base frequency: \( f' = \frac{10}{9} \times 450 = 10 \times 50 = 500 \text{ Hz} \).
Why other options are incorrect:
Option B would be correct if the source were receding (moving away). Option D is the original frequency, incorrectly assuming no Doppler shift occurs.
Ripple tank is used to study features of [NMDCAT 2020]
A
Particle
B
Wave
C
Light
D
Solid
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
A ripple tank is a specialized piece of lab equipment featuring a shallow glass tank of water.
Solution:
It is explicitly designed to generate and visualize 2D mechanical water waves.
By shining a light from above, the shadows of the wave crests and troughs allow students to study core wave behaviors such as reflection, refraction, diffraction, and interference.
Why other options are incorrect:
While light is used to illuminate the tank, the tank's purpose is to study the water waves themselves. Particles and solids do not form the bulk behaviors studied in this tank.
Waves which deal with fast moving elementary particle [NMDCAT 2020]
A
Transverse Waves
B
Longitudinal waves
C
Matter waves
D
Periodic waves
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
According to quantum mechanics (specifically Louis de Broglie's hypothesis), all matter exhibits wave-like properties.
Solution:
When elementary particles (like electrons, protons, or neutrons) travel at high velocities, their wavelength becomes physically significant.
These are formally defined as Matter waves (or de Broglie waves).
Their wavelength is given by \( \lambda = \frac{h}{p} \), where \( p \) is the particle's momentum.
Why other options are incorrect:
Transverse and longitudinal are classifications of macroscopic mechanical or electromagnetic waves, not the quantum probability waves associated with moving elementary particles.
What will be the expression for the observed frequency, if the source is moving towards the observer? [MDCAT 2019]
A
\( f_o = \left(\frac{v}{v-u_s}\right)f \)
B
\( f_o = \left(\frac{v}{v+u_s}\right)f \)
C
\( f_o = \left(\frac{v}{v+u_o}\right)f \)
D
\( f_o = \left(\frac{v}{v-u_o}\right)f_o \)
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
The Doppler Effect predicts a change in observed frequency when there is relative motion. An approaching source compresses the wave fronts in the direction of travel.
Formula:
$$ f_o = \left( \frac{v}{v - u_s} \right) f $$
Solution:
Because the source is moving towards the observer, the waves are "crowded" together. This physically shortens the wavelength.
A shorter apparent wavelength directly results in a higher apparent frequency.
To yield a fraction greater than 1, the denominator must be decreased. Therefore, we subtract the source velocity (\( u_s \)) from the wave velocity (\( v \)) in the denominator.
Why other options are incorrect:
Option B represents a source moving away. Options C and D wrongly place the variables (using observer velocity \( u_o \) in the denominator instead of the numerator).
A shock wave is produced due to an earthquake which makes the building move in the direction of the shock wave. Which progressive wave would this be? [MDCAT 2018]
A
Longitudinal wave
B
Material wave
C
Transverse wave
D
Particle wave
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
Waves are classified based on the direction of medium oscillation relative to the direction of wave propagation.
Solution:
The question states that the building moves strictly "in the direction of the shock wave".
When the particles of the medium (or the building, in this case) oscillate parallel to the direction of energy transport, it defines a longitudinal wave.
In seismology, these are known as Primary (P) waves, which are compressional/longitudinal in nature.
Why other options are incorrect:
Transverse waves (S-waves) cause oscillations perpendicular to the propagation path, which would shake the building side-to-side, not just in the wave's direction.
Which one of the following varies when an object execute simple harmonic motion? [ETEA 2018]
A
Angular frequency
B
Total energy
C
Force
D
Amplitude
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
Simple Harmonic Motion (SHM) requires a restoring force that is directly proportional to displacement.
Formula:
$$ F = -kx $$
Solution:
In ideal SHM, Amplitude and Angular Frequency (\( \omega = \sqrt{k/m} \)) are fundamental constants determined by the system's physical properties.
Total energy (\( E = \frac{1}{2}kx_0^2 \)) is conserved and remains perfectly constant throughout the motion.
However, the restoring Force continuously changes its magnitude and direction depending on the mass's exact instantaneous position (\( x \)), being maximum at extremes and zero at equilibrium.
Why other options are incorrect:
Options A, B, and D define the rigid, unchanging boundary conditions of ideal simple harmonic motion.
Which one of the following is not a characteristic of stationary wave? [ETEA 2018]
A
Half wavelength is the distance between the adjacent nodes
B
Amplitude is not the same
C
Phase is identical between two adjacent nodes
D
Energy of the stationary waves travels outwards
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
Stationary (standing) waves trap energy within fixed physical boundaries rather than transmitting it through space.
Solution:
A defining feature of a stationary wave is that the net power flow across any vertical section is zero. Energy is strictly exchanged between kinetic and potential forms locally within each loop.
Therefore, the statement "Energy of the stationary waves travels outwards" is fundamentally false. It describes a progressive wave, not a stationary one.
Why other options are incorrect:
Option A is true: The distance between two adjacent nodes equals \( rac{\lambda}{2}\) (half the wavelength).
Option B is true: Amplitude varies from zero at nodes to maximum at antinodes.
Option C is true: All particles within a single loop (between two adjacent nodes) oscillate in phase.
A metallic wire of 2m length hooked between two points has tension of 10N. If mass per unit length of wire is 0.004 kg/s then fundamental frequency emitted by wire on vibration is: [MDCAT 2017]
A
12.5 Hz
B
24 Hz
C
48 Hz
D
6.25 Hz
View Answer & Propolis Autopsy
Correct Key: Option ADiagnostic Explanation
Concept:
The fundamental frequency of a stretched string depends on its length, tension, and linear mass density.
Formula:
$$ v = \sqrt{\frac{T}{m}} $$ $$ f_1 = \frac{v}{2L} $$
Solution:
Note: The unit 'kg/s' in the question is a historical typo for mass per unit length, which should be kg/m.
First, find the wave speed: \( v = \sqrt{\frac{10}{0.004}} = \sqrt{\frac{10000}{4}} = \sqrt{2500} = 50 \text{ m/s} \).
Now, apply the fundamental frequency formula with length \( L = 2 \text{ m} \):
Option D occurs if the student forgets the '2' in the denominator. Option C occurs if one mistakenly uses \( L \) in the numerator instead of denominator.
A source of sound moves towards a stationary observer with speed one third speed of sound. If the frequency of the sound from the source is 100 Hz, the apparent frequency of the sound heard by the observer is: [MDCAT 2017]
A
60 Hz
B
200 Hz
C
100 Hz
D
150 Hz
View Answer & Propolis Autopsy
Correct Key: Option DDiagnostic Explanation
Concept:
When a source approaches a stationary observer, the sound waves compress, leading to a higher apparent frequency.
Formula:
$$ f' = \left( \frac{v}{v - v_s} \right) f $$
Solution:
We are given that the source speed \( v_s = \frac{v}{3} \) and true frequency \( f = 100 \text{ Hz} \).
Substitute \( v_s \) into the formula: \( f' = \left( \frac{v}{v - v/3} \right) 100 \).
Simplify the denominator: \( v - \frac{v}{3} = \frac{2v}{3} \).
Using the formula for a receding source (adding in the denominator) yields 75 Hz. Mistakenly putting the speed change in the numerator yields wrong figures entirely.
In a stationary wave the distance between consecutive antinodes is 25 cm. If the wave velocity is 300 ms\(^{-1}\) then the frequency of the wave will be: [ETEA 2017]
A
150 Hz
B
300 Hz
C
600 Hz
D
750 Hz
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
The spatial structure of a standing wave directly dictates its wavelength. The distance between two consecutive antinodes represents exactly half a wavelength.
Formula:
$$ \frac{\lambda}{2} = \text{Distance between antinodes} $$ $$ v = f \lambda $$
Solution:
We are given the distance between antinodes: \( \frac{\lambda}{2} = 25 \text{ cm} \).
Using the wave equation \( f = \frac{v}{\lambda} \), substitute \( v = 300 \text{ m/s} \) and \( \lambda = 0.5 \text{ m} \).
\( f = \frac{300}{0.5} = 600 \text{ Hz} \).
Why other options are incorrect:
Option A assumes 25 cm is the full wavelength (\( 300/0.25 = 1200 \text{ Hz} \), ). If a student assumes 25 cm is \( \lambda/4 \), they get 1 meter, yielding 300 Hz (Option B). Thus, confusing the loop geometry is the primary trap.
The speed of sound in air at NTP is 300m/s. If the air pressure become 4 times then the speed of the sound will be [ETEA 2017]
A
150m/s
B
300m/s
C
600m/s
D
None
View Answer & Propolis Autopsy
Correct Key: Option BDiagnostic Explanation
Concept:
The velocity of sound in an ideal gas depends solely on temperature and the gas's inherent properties, but it is independent of pressure.
Formula:
$$ v = \sqrt{\frac{\gamma P}{\rho}} $$
Solution:
According to Boyle's law (\( P \propto \rho \)), if you increase the pressure of a gas by a factor of 4, the gas gets compressed, causing its density (\( \rho \)) to also increase exactly by a factor of 4.
Because both numerator and denominator in Laplace's formula increase by the exact same multiplier, the ratio \( \frac{P}{\rho} \) remains mathematically constant.
Therefore, the speed remains 300 m/s.
Why other options are incorrect:
Option C assumes speed is directly proportional to pressure, incorrectly doubling the speed.
Standing waves are produced in 10m long stretched string. If the string vibrates in 5 segments and wave velocity is 20ms\(^{-1}\). Its frequency is: [ETEA 2017]
A
2 Hz
B
4 Hz
C
5 Hz
D
10 Hz
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
When a stretched string vibrates in discrete segments (loops), each segment corresponds to half a wavelength.
Formula:
$$ f_n = n \left( \frac{v}{2L} \right) $$
Solution:
We are given string length \( L = 10 \text{ m} \), number of segments \( n = 5 \), and velocity \( v = 20 \text{ m/s} \).
Plug the values into the generalized harmonic formula:
Stationary (or standing) waves are formed by the superposition of two identical waves traveling in opposite directions.
Solution:
Because the two parent waves carry equal amounts of energy in mutually opposite directions, the net flow of energy across any section of the medium is zero.
Energy remains confined between the nodes; thus, there is no transfer of energy through space.
Why other options are incorrect:
Option B is incorrect because energy is not constant at all points; antinodes possess maximum kinetic/potential energy oscillation, while nodes have zero. Option C is wrong because adjacent loops are completely out of phase.
In a vibrating cord the point where the particles are stationary is called [ETEA 2014]
A
Crest
B
Anti-node
C
Node
D
Trough
View Answer & Propolis Autopsy
Correct Key: Option CDiagnostic Explanation
Concept:
When stationary (standing) waves form on a cord, they create an alternating pattern of complete destructive and constructive interference.
Solution:
A Node is a specific point along the standing wave where the interfering waves consistently cancel each other out, resulting in zero net displacement (stationary particles).
An Anti-node is a point of maximum displacement.
Why other options are incorrect:
Crests and troughs are moving features of a progressive wave, whereas nodes represent fixed zero-displacement locations.
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