Ratio of amplitude for two wave is 4:7 .Find the ratio of maximum amplitude to minimum amplitude.

Answer

To solve the problem of finding the ratio of maximum amplitude to minimum amplitude given the ratio of two wave amplitudes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
We are given the ratio of the amplitudes of two waves, \( A_1 \) and \( A_2 \), which is \( \frac{A_1}{A_2} = \frac{4}{7} \).

2. **Assign Values to Amplitudes:**
From the ratio, we can assign:
- \( A_1 = 4k \)
- \( A_2 = 7k \)
where \( k \) is a constant.

3. **Calculate Maximum Amplitude:**
The maximum amplitude \( A_{max} \) is the sum of the two amplitudes:
\[ A_{max} = A_1 + A_2 = 4k + 7k = 11k \]

4. **Calculate Minimum Amplitude:**
The minimum amplitude \( A_{min} \) is the absolute difference of the two amplitudes:
\[ A_{min} = |A_1 - A_2| = |4k - 7k| = | -3k | = 3k \]

5. **Find the Ratio of Maximum Amplitude to Minimum Amplitude:**
Now we can find the ratio of maximum amplitude to minimum amplitude:
\[ \text{Ratio} = \frac{A_{max}}{A_{min}} = \frac{11k}{3k} = \frac{11}{3} \]

6. **Final Answer:**
Therefore, the ratio of maximum amplitude to minimum amplitude is \( \frac{11}{3} \).