Ratio of amplitude for two wave is 7:9 .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 \( A_1 : A_2 = 7 : 9 \).
- This can be expressed as \( \frac{A_1}{A_2} = \frac{7}{9} \).

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 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 Values**:
- Substitute the ratio of amplitudes into the intensity ratio formula:
\[ \frac{I_1}{I_2} = \left( \frac{7}{9} \right)^2 \]

4. **Calculate the Square of the Ratio**:
- Now, calculate \( \left( \frac{7}{9} \right)^2 \):
\[ \frac{I_1}{I_2} = \frac{7^2}{9^2} = \frac{49}{81} \]

5. **Conclusion**:
- Therefore, the ratio of intensities \( I_1 : I_2 \) is:
\[ I_1 : I_2 = 49 : 81 \]

### Final Answer:
The ratio of intensity \( I_1 : I_2 = 49 : 81 \).

---