MHT CET · Physics · Waves and Sound
A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of \(9 \mathrm{~kg}\) is suspended from the wire. When this mass is replaced by a mass \(\mathrm{M}\), the wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of ' \(M\) ' is
- A 5 kg
- B 12.5 kg
- C \(\frac{1}{25} \mathrm{~kg}\)
- D 25 kg
Answer & Solution
Correct Answer
(D) 25 kg
Step-by-step Solution
Detailed explanation
For a vibrating wire, we have \(\mathrm{Tp}^2=\) constant
Where \(\mathrm{p}\) is the number of loops formed and \(\mathrm{T}\) is the tension
\(
\begin{aligned}
& \mathrm{T}_1=9 \mathrm{~kg}-\mathrm{wt}, \mathrm{p}_1=5, \mathrm{p}_2=3 \\
& \therefore \mathrm{T}_1 \mathrm{P}_1^2=\mathrm{T}_2 \mathrm{P}_2^2 \\
& \therefore 9 \times 25=\mathrm{T}_2 \times 9 \\
& \therefore \mathrm{T}_2=25 \mathrm{~kg}-\mathrm{wt}
\end{aligned}
\)
Where \(\mathrm{p}\) is the number of loops formed and \(\mathrm{T}\) is the tension
\(
\begin{aligned}
& \mathrm{T}_1=9 \mathrm{~kg}-\mathrm{wt}, \mathrm{p}_1=5, \mathrm{p}_2=3 \\
& \therefore \mathrm{T}_1 \mathrm{P}_1^2=\mathrm{T}_2 \mathrm{P}_2^2 \\
& \therefore 9 \times 25=\mathrm{T}_2 \times 9 \\
& \therefore \mathrm{T}_2=25 \mathrm{~kg}-\mathrm{wt}
\end{aligned}
\)
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