Wave Mechanics Vibration Of String Question 51
Question: The fundamental frequency of a sonometre wire is n. If its radius is doubled and its tension becomes half, the material of the wire remains same, the new fundamental frequency will be
[BCECE 2005]
Options:
A) n
B) $ \frac{n}{\sqrt{2}} $
C) $ \frac{n}{2} $
D) $ \frac{n}{2\sqrt{2}} $
Show Answer
Answer:
Correct Answer: D
Solution:
$ n=\frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}\rho }} $
Therefore $ n\propto \frac{\sqrt{T}}{r} $
Therefore $ \frac{n _{2}}{n _{1}}=\frac{r _{1}}{r _{2}}\sqrt{\frac{T _{2}}{T _{1}}} $
$ =\frac{1}{2}\times \sqrt{\frac{1}{2}} $ = $ \frac{1}{2\sqrt{2}} $
BETA
