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 $
BETA
