Question

In sonometer experiment, the bridges are separated by a fixed distance. The wire which is slightly elastic, emits a tone of frequency '$n$' when held by tension '$T$'. If the tension is increased to '$4T$', the tone emitted by the wire will be of frequency

• A. $n$
• B. $2n$
• C. Slightly greater than $2n$
• D. Slightly less than $2n$

Answer 1

The correct option is D Slightly less than $2n$

Frequency tone emitted $=n$

$\Rightarrow n=\frac{x}{2L}\sqrt{\frac{T}{\mu }}(x=1,2,3,\mathrm{4.....})$

If $T^1=4T$

Then, $n=\frac{x}{2L}\sqrt{\frac{4T}{\mu }}=2n$

Since the wire is slightly elastic therefore frequency would be slightly less than $2n$.

$\therefore$ Option (D) is correct.