Question

A sonometer wire resonates with a given tuning fork 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 a mass $M,$ the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of $M$ is:

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

Answer 1

Answer: (B)

$F=\frac{n}{2l}\sqrt{T/\mu }$ { $n\to n^{th}$ Harmonic or $n$ anti nodes}
In case $(i)$ $f=\frac{5}{2l}\sqrt{\frac{90}{\mu }}$
In case $(ii)$ $f=\frac{3}{2l}\sqrt{\frac{T}{\mu }}$
$\Rightarrow T=50N$ or $M=5kg$