Ratio of amplitude for two wave is 15:11.Find the ratio of intensity?

Explanation

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

### Step-by-Step Solution:

1. **Identify the Given Data**:
The ratio of amplitudes of two waves is given as \( A_1 : A_2 = 15 : 11 \). This can be expressed as:
\[ \frac{A_1}{A_2} = \frac{15}{11} \]

2. **Understand the Relationship Between Intensity and Amplitude**:
The intensity \( I \) of a wave is directly proportional to the square of its amplitude. This relationship can be expressed mathematically as:
\[ I \propto A^2 \]
Therefore, the ratio of intensities \( I_1 : I_2 \) 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 Known Values**:
We substitute the ratio of amplitudes into the equation for the ratio of intensities:
\[ \frac{I_1}{I_2} = \left(\frac{15}{11}\right)^2 \]

4. **Calculate the Square of the Ratio**:
Now we calculate the square of \( \frac{15}{11} \):
\[ \frac{I_1}{I_2} = \frac{15^2}{11^2} = \frac{225}{121} \]

5. **Final Result**:
Thus, the ratio of intensities \( I_1 : I_2 \) is:
\[ I_1 : I_2 = 225 : 121 \]