Ratio of amplitude for two wave is 10:11 .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 \( A_1 : A_2 = 10 : 11 \).
- We can express this as \( \frac{A_1}{A_2} = \frac{10}{11} \).

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 Values:**
- Now, substituting the value of \( \frac{A_1}{A_2} \):
\[ \frac{I_1}{I_2} = \left( \frac{10}{11} \right)^2 \]

4. **Calculate the Square of the Ratio:**
- Squaring the ratio:
\[ \frac{I_1}{I_2} = \frac{10^2}{11^2} = \frac{100}{121} \]

5. **Final Result:**
- Thus, the ratio of intensities \( I_1 : I_2 \) is:
\[ I_1 : I_2 = 100 : 121 \]

### Summary:
The ratio of intensity for the two waves is \( 100 : 121 \).