Ratio of amplitude for two wave is 5:9 .Find the ratio of maximum amplitude to minimum amplitude.

Answer

To solve the problem, we need to find the ratio of maximum amplitude to minimum amplitude given the ratio of two wave amplitudes.

### Step-by-Step Solution:

1. **Identify the Given Data**:
The ratio of the amplitudes of the two waves is given as:
\[ \frac{A_1}{A_2} = \frac{5}{9} \]
Here, \(A_1\) is the amplitude of the first wave and \(A_2\) is the amplitude of the second wave.

2. **Assign Values to Amplitudes**:
From the ratio, we can assign:
\[ A_1 = 5 \quad \text{and} \quad A_2 = 9 \]

3. **Calculate Maximum Amplitude**:
The maximum amplitude \(A_{\text{max}}\) is calculated by adding the two amplitudes:
\[ A_{\text{max}} = A_1 + A_2 = 5 + 9 = 14 \]

4. **Calculate Minimum Amplitude**:
The minimum amplitude \(A_{\text{min}}\) is calculated by taking the absolute difference of the two amplitudes:
\[ A_{\text{min}} = |A_2 - A_1| = |9 - 5| = 4 \]

5. **Calculate the Ratio of Maximum Amplitude to Minimum Amplitude**:
Now, we can find the ratio of maximum amplitude to minimum amplitude:
\[ \text{Ratio} = \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{14}{4} = \frac{7}{2} \]

### Final Answer:
The ratio of maximum amplitude to minimum amplitude is:
\[ \frac{7}{2} \]