Physics Waves ETEA 2023
PMDC Verified Question 39 of 125
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:
A
100 sec
B
4 sec
C
2 sec
D
0.2 sec
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Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: 0.2 sec
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.

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