Ratio of amplitude for two wave is 5:9 .Find the ratio of intensity?

Answer

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 \( \frac{A_1}{A_2} = \frac{5}{9} \).

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 mathematically as:
\[ I \propto A^2 \]

3. **Express the Ratio of Intensities:**
- From the relationship above, we can write the ratio of intensities \( \frac{I_1}{I_2} \) in terms of the ratio of amplitudes:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

4. **Substitute the Given Ratio of Amplitudes:**
- Now, substitute the value of \( \frac{A_1}{A_2} = \frac{5}{9} \) into the equation:
\[ \frac{I_1}{I_2} = \left(\frac{5}{9}\right)^2 \]

5. **Calculate the Square of the Ratio:**
- Calculate \( \left(\frac{5}{9}\right)^2 \):
\[ \frac{I_1}{I_2} = \frac{25}{81} \]

6. **State the Final Result:**
- Therefore, the ratio of intensities \( \frac{I_1}{I_2} \) is:
\[ \frac{I_1}{I_2} = \frac{25}{81} \]

### Final Answer:
The ratio of intensity \( I_1 : I_2 \) is \( 25 : 81 \).

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