Wave Mechanics Vibration Of String Question 21
Question: In order to double the frequency of the fundamental note emitted by a stretched string, the length is reduced to $ \frac{3}{4} $ th of the original length and the tension is changed. The factor by which the tension is to be changed, is
[EAMCET 2001]
Options:
A) $ \frac{3}{8} $
B) $ \frac{2}{3} $
C) $ \frac{8}{9} $
D) $ \frac{9}{4} $
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Answer:
Correct Answer: D
Solution:
$ n=\frac{1}{2l}\sqrt{\frac{T}{m}}\Rightarrow n\propto \frac{\sqrt{T}}{l} $
Therefore $ \frac{T _{2}}{T _{1}}={{( \frac{n _{2}}{n _{1}} )}^{2}}{{( \frac{l _{2}}{l _{1}} )}^{2}}={{(2)}^{2}}{{( \frac{3}{4} )}^{2}}=\frac{9}{4} $
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