Question

A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9 \,kg$ is suspended from the wire. When this mass is replaced by a mass $M$, the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of $M$

• A. 25 kg
• B. 5 kg
• C. 12.5 kg
• D. 1/25 kg
• E. 1/5 kg

Answer 1

Answer: (A)

Frequency of vibration of vibration of string,
$n =\frac{ p }{2 l } \sqrt{\frac{ T }{ m }}$
No. of loops $=$ No. of antinodes
For, $p =5$
$T =9 \,g$
$\therefore n _{1}=\frac{5}{2 l } \sqrt{\frac{9 g }{ m }}$
For, $p =3$
$T = Mg$
$\therefore n _{2}=\frac{3}{2 l } \sqrt{\frac{ Mg }{ m }}$
$n _{1} \,n _{2}$
$\therefore \frac{5}{21} \sqrt{\frac{9 g}{ M }}=\frac{3}{21} \sqrt{\frac{ Mg }{ m }}$
$\Rightarrow M =25 \,kg$