Question

Fundamental frequency of a sonometer wire is n. If the length and diameter of the wire are doubled 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. $\frac{2n}{\sqrt{2}}$

Answer 1

The correct option is C $\frac{n}{4}$

Frequency of vibration of sonometer wire is given as

$n=\frac{1}{2l}\sqrt{\frac{T}{m}}=\frac{1}{2l}\sqrt{\frac{T}{\pi r^{2}d}}\Rightarrow n\propto \frac{1}{\sqrt{\left(d\right)}}$

If the length and diameter of the wire are doubled. The new frequency will be $\frac{n}{4}$.