Ratio of amplitude for two wave is 1:3 .Find the ratio of intensity?

Explanation

To find the ratio of intensity for two waves given the ratio of their amplitudes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
The ratio of amplitudes for two waves is given as:
\[ \frac{A_1}{A_2} = \frac{1}{3} \]

2. **Understand the Relationship Between Intensity and Amplitude**:
We know that the intensity \( I \) of a wave is proportional to the square of its amplitude \( A \):
\[ I \propto A^2 \]
This means that:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

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

4. **Calculate the Ratio of Intensities**:
Now calculate the square of the ratio:
\[ \frac{I_1}{I_2} = \frac{1^2}{3^2} = \frac{1}{9} \]

5. **Express the Final Ratio**:
Therefore, the ratio of intensities \( I_1 : I_2 \) is:
\[ I_1 : I_2 = 1 : 9 \]

### Final Answer:
The ratio of intensity \( I_1 : I_2 \) is \( 1 : 9 \).

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