Ratio of amplitude for two wave is 8:6 .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 \( A_1 : A_2 = 8 : 6 \).

2. **Express the Ratio of Amplitudes:**
- We can express this ratio in fractional form:
\[ \frac{A_1}{A_2} = \frac{8}{6} \]

3. **Understand the Relationship Between Intensity and Amplitude:**
- Intensity \( I \) is directly proportional to the square of the amplitude. This can be expressed mathematically as:
\[ I \propto A^2 \]
Therefore, the ratio of intensities can be expressed as:
\[ \frac{I_1}{I_2} = \left(\frac{A_1}{A_2}\right)^2 \]

4. **Substitute the Ratio of Amplitudes into the Intensity Formula:**
- Now we substitute the ratio of amplitudes into the intensity formula:
\[ \frac{I_1}{I_2} = \left(\frac{8}{6}\right)^2 \]

5. **Calculate the Square of the Ratio:**
- Squaring the fraction gives:
\[ \frac{I_1}{I_2} = \frac{8^2}{6^2} = \frac{64}{36} \]

6. **Simplify the Ratio (if necessary):**
- The ratio \( \frac{64}{36} \) can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[ \frac{64 \div 4}{36 \div 4} = \frac{16}{9} \]

7. **Final Result:**
- Thus, the ratio of intensities \( I_1 : I_2 = 64 : 36 \) or simplified \( 16 : 9 \).

### Final Answer:
The ratio of intensity \( I_1 : I_2 = 64 : 36 \) or simplified \( 16 : 9 \).