Ratio of amplitude for two wave is 8:2 .Find the ratio of intensity?

Explanation

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 \( A_1 : A_2 = 8 : 2 \).

2. **Express the Ratio of Amplitudes:**
- We can express this ratio mathematically as:
\[ \frac{A_1}{A_2} = \frac{8}{2} = 4 \]

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 can be expressed in terms of the ratio of amplitudes:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

4. **Substitute the Ratio of Amplitudes:**
- Now, substitute the value of \( \frac{A_1}{A_2} \) into the equation for intensity:
\[ \frac{I_1}{I_2} = \left(\frac{8}{2}\right)^2 \]

5. **Calculate the Square of the Ratio:**
- Calculate \( \left(\frac{8}{2}\right)^2 \):
\[ \frac{I_1}{I_2} = \left(4\right)^2 = 16 \]

6. **Final Result:**
- Thus, the ratio of intensities \( I_1 : I_2 \) is:
\[ I_1 : I_2 = 16 : 1 \]