Physics Waves ETEA 2023
PMDC Verified Question 37 of 125
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?
A
2T
B
4T
C
8T
D
16T
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option B: 4T
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.

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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