Question

The fundamental frequency of a sonometer wire is $n$ . If the length and diameter of the wire are double keeping the tension same, then the new fundamental frequency is

• A. $\frac{n}{2\sqrt{2}}$
• B. $\sqrt{2}n$
• C. $\frac{n}{4}$
• D. $\frac{n}{2}$

Answer 1

Answer: (C)

Frequency of vibration of sonometer wire is given as
$n=\frac{1}{2l}\sqrt{\frac{T}{m}}=\frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}d}}$
$\Rightarrow n\propto \frac{1}{\sqrt{d}}$ $n\propto \frac{1}{r}andn\propto \frac{1}{l}$
If the length and diameter of the wire are doubled.
The new frequency will be $\frac{n}{4}$ .