Ratio of amplitude for two wave is 7:9 .Find the ratio of maximum amplitude to minimum amplitude.

Answer

To solve the problem, we need to find the ratio of the maximum amplitude to the minimum amplitude given the ratio of the amplitudes of two waves.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- The ratio of the amplitudes of two waves is given as \( A_1 : A_2 = 7 : 9 \).
- This means we can represent the amplitudes as:
- \( A_1 = 7k \)
- \( A_2 = 9k \)
where \( k \) is a common factor.

2. **Calculate Maximum Amplitude:**
- The maximum amplitude \( A_{max} \) is calculated by adding the two amplitudes:
\[ A_{max} = A_1 + A_2 = 7k + 9k = 16k \]

3. **Calculate Minimum Amplitude:**
- The minimum amplitude \( A_{min} \) is calculated by taking the difference of the two amplitudes:
\[ A_{min} = A_2 - A_1 = 9k - 7k = 2k \]

4. **Calculate the Ratio of Maximum Amplitude to Minimum Amplitude:**
- Now, we can find the ratio of maximum amplitude to minimum amplitude:
\[ \text{Ratio} = \frac{A_{max}}{A_{min}} = \frac{16k}{2k} \]
- Simplifying this gives:
\[ \text{Ratio} = \frac{16}{2} = 8 \]

5. **Final Result:**
- Therefore, the ratio of maximum amplitude to minimum amplitude is \( 8 : 1 \).