A tuning fork of frequency 480Hz is used to vibrate a sonometer wire having natural frequency 240 Hz. The wire will vibrate with a frequency of

Options

A. 240Hz
B. 480Hz
C. 720Hz
D. will not vibrate

Answer

To solve the problem, we need to determine the frequency at which the sonometer wire will vibrate when it is excited by a tuning fork of frequency 480 Hz. The sonometer wire has a natural frequency of 240 Hz.

### Step-by-Step Solution:

1. **Understand the Concept of Natural Frequency**:
- The natural frequency of an object is the frequency at which it tends to vibrate when not subjected to continuous external forces. In this case, the sonometer wire has a natural frequency of 240 Hz.

2. **Identify the Frequency of the Tuning Fork**:
- The tuning fork is vibrating at a frequency of 480 Hz. This is the frequency that will be applied to the sonometer wire.

3. **Determine the Frequency of the Wire**:
- When a tuning fork is applied to a sonometer wire, the wire will vibrate at the frequency of the tuning fork, provided that the tuning fork's frequency is greater than the natural frequency of the wire.
- In this case, since the tuning fork frequency (480 Hz) is greater than the natural frequency of the wire (240 Hz), the wire will vibrate at the frequency of the tuning fork.

4. **Conclusion**:
- Therefore, the frequency at which the sonometer wire will vibrate is 480 Hz.

### Final Answer:
The wire will vibrate with a frequency of **480 Hz**.

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