Ratio of amplitude for two wave is 15:10.Find the ratio of intensity?

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Data:**
- The ratio of amplitudes of two waves is given as \( A_1 : A_2 = 15 : 10 \).

2. **Express the Ratio of Amplitudes:**
- We can express this ratio mathematically as:
\[ \frac{A_1}{A_2} = \frac{15}{10} \]

3. **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 expressed as:
\[ \frac{I_1}{I_2} = \left( \frac{A_1}{A_2} \right)^2 \]

4. **Substitute the Ratio of Amplitudes:**
- Now, substituting the ratio of amplitudes into the intensity ratio formula:
\[ \frac{I_1}{I_2} = \left( \frac{15}{10} \right)^2 \]

5. **Calculate the Square of the Ratio:**
- Now, calculate \( \left( \frac{15}{10} \right)^2 \):
\[ \frac{I_1}{I_2} = \frac{15^2}{10^2} = \frac{225}{100} \]

6. **Simplify the Ratio:**
- The ratio \( \frac{225}{100} \) can be simplified if needed, but it is already in a clear form. Thus, the final ratio of intensities is:
\[ \frac{I_1}{I_2} = \frac{225}{100} \]

### Final Answer:
The ratio of intensity \( I_1 : I_2 \) is \( 225 : 100 \).

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