Ratio of amplitude for two wave is 11:1 .Find the ratio of intensity?

Explanation

To solve the problem of finding the ratio of intensity given the ratio of amplitudes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
- The ratio of the amplitudes of the two waves is given as \( A_1 : A_2 = 11 : 1 \).

2. **Express the Ratio of Amplitudes**:
- We can express this ratio mathematically as:
\[ \frac{A_1}{A_2} = \frac{11}{1} \]

3. **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 can be expressed in terms of the ratio of amplitudes:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

4. **Substitute the Ratio of Amplitudes into the Intensity Ratio**:
- Now, substituting the value of \( \frac{A_1}{A_2} \):
\[ \frac{I_1}{I_2} = \left(\frac{11}{1}\right)^2 \]

5. **Calculate the Square**:
- Performing the square calculation:
\[ \frac{I_1}{I_2} = \frac{121}{1} \]

6. **Final Result**:
- Therefore, the ratio of intensities \( I_1 : I_2 \) is:
\[ I_1 : I_2 = 121 : 1 \]

### Final Answer:
The ratio of intensity \( I_1 : I_2 \) is \( 121 : 1 \).

---