Ratio of amplitude for two wave is 3:9 .Find the ratio of intensity?

Answer

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 amplitudes of the two waves is given as:
\[ \frac{A_1}{A_2} = \frac{3}{9} \]

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

3. **Substitute the Given Ratio of Amplitudes**:
We substitute the value of \(\frac{A_1}{A_2}\) into the intensity ratio formula:
\[ \frac{I_1}{I_2} = \left(\frac{3}{9}\right)^2 \]

4. **Calculate the Square of the Ratio**:
First, simplify \(\frac{3}{9}\):
\[ \frac{3}{9} = \frac{1}{3} \]
Now, calculate the square:
\[ \left(\frac{1}{3}\right)^2 = \frac{1}{9} \]

5. **Final Result**:
Thus, the ratio of intensities is:
\[ \frac{I_1}{I_2} = \frac{1}{9} \]

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