Ratio of amplitude for two wave is 1:5 .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 \( A_1 : A_2 = 1 : 5 \).
- This means we can express the amplitudes as \( A_1 = 1k \) and \( A_2 = 5k \) for some constant \( k \).

2. **Determine Maximum and Minimum Amplitudes:**
- The maximum amplitude \( A_{\text{max}} \) is calculated using the formula:
\[ A_{\text{max}} = A_1 + A_2 \]
- The minimum amplitude \( A_{\text{min}} \) is calculated using the formula:
\[ A_{\text{min}} = A_2 - A_1 \]
- Substituting the values:
\[ A_{\text{max}} = A_1 + A_2 = 1k + 5k = 6k \]
\[ A_{\text{min}} = A_2 - A_1 = 5k - 1k = 4k \]

3. **Calculate the Ratio of Maximum Amplitude to Minimum Amplitude:**
- Now, we need to find the ratio:
\[ \text{Ratio} = \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{6k}{4k} \]
- The \( k \) cancels out:
\[ \text{Ratio} = \frac{6}{4} = \frac{3}{2} \]

4. **Final Answer:**
- The ratio of maximum amplitude to minimum amplitude is \( 3 : 2 \).