The average power transmitted through a given point on a string supporting a sine wave is 0.20 W when the amplitude of the wave is 2.0 mm. What power will be transmitted through this point if the amplitude is increased to 3.0 mm.

Explanation

To solve the problem step by step, we will use the relationship between the power transmitted through a wave and its amplitude. The power \( P \) transmitted through a wave is proportional to the square of its amplitude \( A \).

### Step-by-Step Solution:

1. **Identify the given values**:
- Initial power \( P_1 = 0.20 \, \text{W} \)
- Initial amplitude \( A_1 = 2.0 \, \text{mm} = 0.002 \, \text{m} \)
- New amplitude \( A_2 = 3.0 \, \text{mm} = 0.003 \, \text{m} \)
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