Ratio of amplitude for two wave is 9:11 .Find the ratio of intensity?

Answer

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**:
We are given the ratio of amplitudes of two waves, which is \( A_1 : A_2 = 9 : 11 \).

2. **Express the Amplitude Ratio**:
We can express the amplitude ratio mathematically as:
\[ \frac{A_1}{A_2} = \frac{9}{11} \]

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

4. **Substitute the Amplitude Ratio**:
Now, substituting the amplitude ratio into the intensity ratio formula:
\[ \frac{I_1}{I_2} = \left(\frac{9}{11}\right)^2 \]

5. **Calculate the Square**:
Now, we calculate the square of the ratio:
\[ \frac{I_1}{I_2} = \frac{9^2}{11^2} = \frac{81}{121} \]

6. **Final Result**:
Thus, the ratio of the intensities \( I_1 : I_2 \) is:
\[ I_1 : I_2 = 81 : 121 \]

### Final Answer:
The ratio of intensity is \( 81 : 121 \).