Physics Waves ETEA 2017
PMDC Verified Question 110 of 125
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:
A
2 Hz
B
4 Hz
C
5 Hz
D
10 Hz
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: 5 Hz
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:


  • \( f_5 = 5 \times \left( \frac{20}{2 \times 10} \right) \).


  • \( f_5 = 5 \times \left( \frac{20}{20} \right) = 5 \times 1 = 5 \text{ Hz} \).


Why other options are incorrect:

Option D arises if a student forgets the 2 in the denominator. Option A calculates only the fundamental frequency (\( n=1 \)).

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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