Ratio of amplitude for two wave is 7:11 .Find the ratio of maximum amplitude to minimum amplitude.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the Given Data
We are given the ratio of the amplitudes of two waves, \( A_1 \) and \( A_2 \), which is \( 7:11 \). This means:
- \( A_1 = 7 \)
- \( A_2 = 11 \)

### Step 2: Calculate the Maximum Amplitude
The maximum amplitude \( A_{\text{max}} \) is calculated by adding the two amplitudes together:
\[ A_{\text{max}} = A_1 + A_2 = 7 + 11 = 18 \]

### Step 3: Calculate the Minimum Amplitude
The minimum amplitude \( A_{\text{min}} \) is calculated by finding the absolute difference between the two amplitudes:
\[ A_{\text{min}} = |A_2 - A_1| = |11 - 7| = 4 \]

### Step 4: Calculate the Ratio of Maximum Amplitude to Minimum Amplitude
Now, we will find the ratio of the maximum amplitude to the minimum amplitude:
\[ \text{Ratio} = \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{18}{4} \]

### Step 5: Simplify the Ratio
To simplify the ratio \( \frac{18}{4} \):
\[ \frac{18}{4} = \frac{9}{2} \]

### Final Answer
The ratio of the maximum amplitude to the minimum amplitude is \( 9:2 \).

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