First slide

Sonometer

Question

A sonometer wire is vibrating with a frequency of 30 Hz in the fundamental mode. If the length of the wire is increased by 20%, the change in frequency of the fundamental mode is

Moderate

A

15 Hz
B

2 Hz
C

5 Hz
D

10 Hz

Solution

Original frequency $f = \frac{1}{2 L} \sqrt{\frac{T}{μ}}$
Final frequency $f^{1} = \frac{1}{2 L^{1}} \sqrt{T / μ}$
$∴ \frac{f^{1}}{f} = \frac{L}{L^{1}} = \frac{L}{1.20 L} = \frac{5}{6} \Rightarrow f^{1} = 5 f / 6$
$∴ f - f^{1} = f - \frac{5 f}{6} = \frac{f}{6} = \frac{30}{6} H z = 5 H z$

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