Ratio of amplitude for two wave is 11:6.Find the ratio of intensity?

Explanation

To solve the problem of finding the ratio of intensity given the ratio of amplitudes of two waves, 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 \( \frac{A_1}{A_2} = \frac{11}{6} \).

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

3. **Substitute the Given Ratio of Amplitudes**:
- Substitute the value of \( \frac{A_1}{A_2} \) into the intensity ratio formula:
\[ \frac{I_1}{I_2} = \left(\frac{11}{6}\right)^2 \]

4. **Calculate the Square of the Ratio**:
- Now, calculate \( \left(\frac{11}{6}\right)^2 \):
\[ \left(\frac{11}{6}\right)^2 = \frac{11^2}{6^2} = \frac{121}{36} \]

5. **Final Result**:
- Therefore, the ratio of intensities \( \frac{I_1}{I_2} \) is:
\[ \frac{I_1}{I_2} = \frac{121}{36} \]

### Conclusion:
The ratio of intensity for the two waves is \( \frac{121}{36} \).

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