Wave Mechanics Vibration Of String Question 46
Question: If the tension and diameter of a sonometer wire of fundamental frequency n are doubled and density is halved then its fundamental frequency will become
[CBSE PMT 2001]
Options:
A) $ \frac{n}{4} $
B) $ \sqrt{2}n $
C) n
D) $ \frac{n}{\sqrt{2}} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ n=\frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}\rho }}\propto \sqrt{\frac{T}{r^{2}\rho }} $
Therefore $ \frac{n _{1}}{n _{2}}=\sqrt{( \frac{T _{1}}{T _{2}} ){{( \frac{r _{2}}{r _{1}} )}^{2}}( \frac{{\rho _{2}}}{{\rho _{1}}} )}=\sqrt{( \frac{1}{2} ){{( \frac{2}{1} )}^{2}}( \frac{1}{2} )}=1 $ \ $ n _{1}=n _{2} $
BETA
