Ratio of amplitude for two wave is 3:7 .Find the ratio of intensity?

Answer

To find the ratio of intensity for two waves given the ratio of their amplitudes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
- The ratio of amplitudes of the two waves is given as \( \frac{A_1}{A_2} = \frac{3}{7} \).

2. **Understand the Relationship Between Intensity and Amplitude**:
- The intensity \( I \) of a wave is directly proportional to the square of its amplitude. This can be expressed mathematically as:
\[ I \propto A^2 \]
- Therefore, the ratio of intensities \( \frac{I_1}{I_2} \) can be expressed in terms of the ratio of amplitudes:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

3. **Substitute the Given Ratio of Amplitudes**:
- Substitute \( \frac{A_1}{A_2} = \frac{3}{7} \) into the intensity ratio formula:
\[ \frac{I_1}{I_2} = \left(\frac{3}{7}\right)^2 \]

4. **Calculate the Square of the Ratio**:
- Calculate \( \left(\frac{3}{7}\right)^2 \):
\[ \frac{I_1}{I_2} = \frac{3^2}{7^2} = \frac{9}{49} \]

5. **Final Result**:
- Therefore, the ratio of intensities \( I_1 : I_2 \) is:
\[ \frac{I_1}{I_2} = \frac{9}{49} \]

### Conclusion:
The ratio of intensity for the two waves is \( 9 : 49 \).

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