Ratio of amplitude for two wave is 11:1 .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 two wave amplitudes.

### Step-by-Step Solution:

1. **Identify the Given Data:**
We are given the ratio of two wave amplitudes, \( A_1 : A_2 = 11 : 1 \).
- This means \( A_1 = 11 \) and \( A_2 = 1 \).

2. **Calculate Maximum Amplitude:**
The maximum amplitude \( A_{\text{max}} \) is calculated using the formula:
\[ A_{\text{max}} = A_1 + A_2 \]
Substituting the values:
\[ A_{\text{max}} = 11 + 1 = 12 \]

3. **Calculate Minimum Amplitude:**
The minimum amplitude \( A_{\text{min}} \) is calculated using the formula:
\[ A_{\text{min}} = A_1 - A_2 \]
Substituting the values:
\[ A_{\text{min}} = 11 - 1 = 10 \]

4. **Calculate the Ratio of Maximum Amplitude to Minimum Amplitude:**
Now, we find the ratio of maximum amplitude to minimum amplitude:
\[ \text{Ratio} = \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{12}{10} \]
Simplifying this ratio:
\[ \text{Ratio} = \frac{12}{10} = \frac{6}{5} \]

### Final Answer:
The ratio of maximum amplitude to minimum amplitude is \( \frac{6}{5} \).

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