Ratio of amplitude for two wave is 1:5 .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 two waves is given as \( A_1 : A_2 = 1 : 5 \).
- This can be expressed as \( \frac{A_1}{A_2} = \frac{1}{5} \).

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 mathematically expressed as:
\[ I \propto A^2 \]
- Therefore, the ratio of intensities \( I_1 \) and \( I_2 \) can be expressed as:
\[ \frac{I_1}{I_2} = \left( \frac{A_1}{A_2} \right)^2 \]

3. **Substitute the Values:**
- Substitute the ratio of amplitudes into the intensity ratio formula:
\[ \frac{I_1}{I_2} = \left( \frac{1}{5} \right)^2 \]

4. **Calculate the Square:**
- Calculate \( \left( \frac{1}{5} \right)^2 \):
\[ \frac{I_1}{I_2} = \frac{1^2}{5^2} = \frac{1}{25} \]

5. **Conclusion:**
- The ratio of intensities \( I_1 : I_2 \) is therefore \( 1 : 25 \).

### Final Answer:
The ratio of intensity is \( 1 : 25 \).