Wave Mechanics Question 768
Question: Fundamental frequency of sonometer wire is n. If the length, tension and diameter of wire are tripled, the new fundamental frequency is
[DPMT 2002]
Options:
A) $ \frac{n}{\sqrt{3}} $
B) $ \frac{n}{3} $
C) $ n\sqrt{3} $
D) $ \frac{n}{3\sqrt{3}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ n=\frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}\rho }}\Rightarrow n\propto \frac{\sqrt{T}}{lr} $
Therefore $ \frac{n _{1}}{n _{2}}=\sqrt{\frac{T _{1}}{T _{2}}}\times \frac{l _{2}}{l _{1}}\times \frac{r _{2}}{r _{1}} $
$ =\sqrt{\frac{T}{3T}}\times \frac{3l}{l}\times \frac{2r}{r}=3\sqrt{3} $
Therefore $ n _{2}=\frac{n}{3\sqrt{3}} $
BETA
