Ratio of amplitude for two wave is 5:11 .Find the ratio of maximum amplitude to minimum amplitude.

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Understand the Given Data
We are given the ratio of the amplitudes of two waves, \( A_1 \) and \( A_2 \), as follows:
\[ \frac{A_1}{A_2} = \frac{5}{11} \]
From this, we can assign values to \( A_1 \) and \( A_2 \):
- Let \( A_1 = 5k \)
- Let \( A_2 = 11k \)
where \( k \) is a common factor.

### Step 2: Calculate Maximum Amplitude
The maximum amplitude \( A_{\text{max}} \) is the sum of the two amplitudes:
\[ A_{\text{max}} = A_1 + A_2 \]
Substituting the values of \( A_1 \) and \( A_2 \):
\[ A_{\text{max}} = 5k + 11k = 16k \]

### Step 3: Calculate Minimum Amplitude
The minimum amplitude \( A_{\text{min}} \) is the absolute difference between the two amplitudes:
\[ A_{\text{min}} = |A_1 - A_2| \]
Substituting the values of \( A_1 \) and \( A_2 \):
\[ A_{\text{min}} = |5k - 11k| = | -6k | = 6k \]

### Step 4: Find the Ratio of Maximum Amplitude to Minimum Amplitude
Now, we can find the ratio of the maximum amplitude to the minimum amplitude:
\[ \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{16k}{6k} \]
The \( k \) cancels out:
\[ \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{16}{6} = \frac{8}{3} \]

### Final Answer
Thus, the ratio of the maximum amplitude to the minimum amplitude is:
\[ \frac{8}{3} \]