Wave Mechanics Vibration Of String Question 39

Question: The frequency of transverse vibrations in a stretched string is 200 Hz. If the tension is increased four times and the length is reduced to one-fourth the original value, the frequency of vibration will be

[EAMCET (Med.) 1999]

Options:

A) 25 Hz

B) 200 Hz

C) 400 Hz

D) 1600 Hz

Show Answer

Answer:

Correct Answer: D

Solution:

$ n=\frac{1}{2l}\sqrt{\frac{T}{m}} $

Therefore $ \frac{n _{1}}{n _{2}}=\frac{l _{2}}{l _{1}}\sqrt{\frac{T _{1}}{T _{2}}} $

$ =\frac{1}{4}\sqrt{\frac{1}{4}}=\frac{1}{8} $

Therefore $ n _{2}=8n _{1}=8\times 200=1600Hz $