Question

A sonometre wire resonates with a given tuning forck forming standing waves with five antinodes between the two bridges when a mass of $9kg$is suspended from the wire. When this mass is replaced by mass $M$, the wire resonates with the same positions of the bridges. Then find the value of square roof of $M$.

• A. $5$
• B. $10$
• C. $25$
• D. $None$

Answer 1

The correct option is C $25$

The frequency of vibration of a string

$n=\frac{p}{2l}\sqrt{\frac{T}{m}}$

Also number of loops = Number of antinodes.

Hence with 5 antinodes and hanging mass of 9 kg. we have p=5 and T=9g

So,

$n_1=\frac{5}{2l}\sqrt{\frac{9g}{m}}$

With 3 antinodes and hanging mass M we have p=3 and T=Mg so,

$n_2=\frac{3}{2l}\sqrt{\frac{Mg}{m}}$

$\because n_1=n_2$

$\frac{5}{2l}\sqrt{\frac{9g}{m}}=\frac{3}{2l}\sqrt{\frac{Mg}{m}}$

Squaring both side we get

$25\times 9=9\times M$

$M=25kg$