A tuning fork of frequency 480 Hz is used to vibrate a sonometer wire having naturl frequency 410 Hz. The wire wil vibrate with frequency

Options

A. 410Hz
B. 480Hz
C. 820Hz
D. 960Hz

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 natural frequency of the wire is given as 410 Hz.

### Step-by-Step Solution:

1. **Understand the Setup**: We have a tuning fork with a frequency of 480 Hz and a sonometer wire with a natural frequency of 410 Hz. The tuning fork is used to vibrate the wire.

2. **Identify the Principle of Vibration**: When a tuning fork vibrates, it creates sound waves at its frequency. When the wire is connected to the tuning fork, it will vibrate in response to these sound waves.

3. **Determine the Frequency of Vibration**: The frequency at which the wire vibrates will match the frequency of the tuning fork. This is because the tuning fork forces the wire to vibrate at its frequency, regardless of the wire's natural frequency.

4. **Conclusion**: Since the tuning fork has a frequency of 480 Hz, the sonometer wire will also vibrate at this frequency.

Thus, the frequency at which the wire will vibrate is **480 Hz**.

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

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