A cork floting in a clam pond executes simple harmonic motion of frequency v when a wsave generated by a boat passes by it. The frequency of the wave is

Options

A. v
B. v/2
C. 2v
D. `sqrt2v`

Answer

To solve the problem, we need to understand the relationship between the frequency of the cork's oscillation and the frequency of the wave passing by it.

### Step-by-Step Solution:

1. **Understanding Simple Harmonic Motion (SHM)**:
- The cork floating on the pond executes simple harmonic motion with a frequency \( v \). This means that the cork moves up and down in a periodic manner with a specific frequency.

2. **Wave Properties**:
- When a wave travels through a medium (in this case, water), it has a certain frequency and wavelength. The relationship between wave speed \( v \), frequency \( f \), and wavelength \( \lambda \) is given by the equation:
\[ v = f \cdot \lambda \]
- Here, \( v \) is the speed of the wave, \( f \) is the frequency of the wave, and \( \lambda \) is the wavelength.

3. **Cork and Wave Interaction**:
- As the wave generated by the boat passes by the cork, the cork experiences the wave and starts to oscillate. The cork's oscillation frequency is equal to the frequency of the wave that is passing by it.

4. **Equating Frequencies**:
- Since the cork is in simple harmonic motion due to the wave, the frequency of the cork's motion \( v \) must be equal to the frequency of the wave \( f \). Therefore, we can write:
\[ f = v \]

5. **Conclusion**:
- Thus, the frequency of the wave generated by the boat is equal to the frequency of the cork's oscillation, which is \( v \).

### Final Answer:
The frequency of the wave is \( v \).

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