Ratio of amplitude for two wave is 11:4 .Find the ratio of maximum amplitude to minimum amplitude.

Explanation

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. **Write Down the Given Ratio**:
We are given the ratio of the amplitudes of two waves, which is \( A_1 : A_2 = 11 : 4 \).

2. **Assign Values to Amplitudes**:
From the ratio, we can assign:
\[ A_1 = 11k \quad \text{and} \quad A_2 = 4k \]
where \( k \) is a common factor.

3. **Calculate Maximum Amplitude**:
The maximum amplitude \( A_{\text{max}} \) is the sum of the two amplitudes:
\[ A_{\text{max}} = A_1 + A_2 = 11k + 4k = 15k \]

4. **Calculate Minimum Amplitude**:
The minimum amplitude \( A_{\text{min}} \) is the absolute difference between the two amplitudes:
\[ A_{\text{min}} = |A_1 - A_2| = |11k - 4k| = 7k \]

5. **Find the Ratio of Maximum Amplitude to Minimum Amplitude**:
Now, we can find the ratio of maximum amplitude to minimum amplitude:
\[ \text{Ratio} = \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{15k}{7k} = \frac{15}{7} \]

### Final Answer:
The ratio of maximum amplitude to minimum amplitude is \( \frac{15}{7} \).

---