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

Answer 1

Answer: (C)

$\frac{n}{4}$

Answer 2

Frequency of vibration of sonometer wire is given as $n=\frac{1}{2l} \sqrt{\frac{T}{m}}=\frac{1}{2l} \sqrt{\frac{T}{\pi r^{2} d}}$ $\Rightarrow n \propto \frac{1}{\sqrt{(d)}}$ $n \propto \frac{1}{r}$ and $n\, 0 \propto \frac{1}{l}$ If the length and diameter of the wire are doubled. The new frequency will be $\frac{n}{4}$