Ratio of amplitude for two wave is 1:2 .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 \( A_1 \) and \( A_2 \) as \( 1:2 \).

### Step-by-step Solution:

1. **Identify the Given Data:**
- The ratio of the amplitudes is given as \( A_1 : A_2 = 1 : 2 \).
- We can denote \( A_1 = 1k \) and \( A_2 = 2k \) for some constant \( k \).

2. **Calculate Maximum Amplitude (\( A_{max} \)):**
- The maximum amplitude when two waves interfere constructively is given by the formula:
\[ A_{max} = A_1 + A_2 \]
- Substituting the values:
\[ A_{max} = 1k + 2k = 3k \]

3. **Calculate Minimum Amplitude (\( A_{min} \)):**
- The minimum amplitude when two waves interfere destructively is given by the formula:
\[ A_{min} = |A_1 - A_2| \]
- Substituting the values:
\[ A_{min} = |1k - 2k| = | -1k | = 1k \]

4. **Find the Ratio of Maximum Amplitude to Minimum Amplitude:**
- Now, we can find the ratio:
\[ \text{Ratio} = \frac{A_{max}}{A_{min}} = \frac{3k}{1k} = 3 \]
- Therefore, the ratio of maximum amplitude to minimum amplitude is:
\[ A_{max} : A_{min} = 3 : 1 \]

### Final Answer:
The ratio of maximum amplitude to minimum amplitude is \( 3 : 1 \).