Question

A sonometer wire resonates with a given tuning fork forming standing waves with 5 antinodes when mass of 9 kg is suspended from the wire. When mass \( M \) is suspended from the wire with same fork and same length between two bridges, 3 antinodes are formed. The mass \( M \) is

• A. 25 kg
• B. 20 kg
• C. 15 kg
• D. 10 kg

Hint:

For same frequency, number of loops varies as square root of tension.

Answer 1

The Correct Option is A

Step 1: Use frequency relation for sonometer wire.
\[ f = \frac{n}{2L}\sqrt{\frac{T}{\mu}} \]
Step 2: Apply same tuning fork condition.
Since frequency and length are same: \[ n_1 \sqrt{T_1} = n_2 \sqrt{T_2} \]
Step 3: Substitute given values.
\[ 5 \sqrt{9} = 3 \sqrt{M} \]
Step 4: Solve for \( M \).
\[ 15 = 3\sqrt{M} \Rightarrow \sqrt{M} = 5 \Rightarrow M = 25 \]
Step 5: Conclusion.
The value of mass \( M \) is \( 25\,\text{kg} \).