Question

A sonometer wire resonates with a given tuning fork forms a standing wave with $5$ nodes between two bridges when a $9kg$ weight is suspended from the wire. When the mass is replaces by a mass $M$, the wire resonates with the same tuning fork forming $3$ nodes for the same position of wedges. The value of $M$ is

• A. $2.25kg$
• B. $5kg$
• C. $12.5kg$
• D. $\frac{1}{25}kg$

Answer 1

Answer: (A)

$2.25kg$

$f=\frac{n_1}{2l}\sqrt{\frac{T_1}{\mu }}=\frac{n_2}{2l}\sqrt{\frac{T_2}{\mu }}\sqrt{\frac{T_1}{T_2}}=\frac{n_2}{n_1}$

Or $\frac{T_1}{T_2}=\frac{n_2^2}{n_1^2}={\left(\frac{4}{2}\right)}^{2}M=\frac{9}{4}=2.25kg$