Ratio of amplitude for two wave is 3:9 .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 amplitudes of two waves, which is:
\[ \frac{A_1}{A_2} = \frac{3}{9} \]
From this, we can deduce that:
- \( A_1 = 3 \)
- \( A_2 = 9 \)

### Step 2: Calculate Maximum Amplitude
The maximum amplitude (\( A_{\text{max}} \)) is calculated by adding the two amplitudes:
\[ A_{\text{max}} = A_1 + A_2 \]
Substituting the values we have:
\[ A_{\text{max}} = 3 + 9 = 12 \]

### Step 3: Calculate Minimum Amplitude
The minimum amplitude (\( A_{\text{min}} \)) is calculated by taking the absolute difference between the two amplitudes:
\[ A_{\text{min}} = |A_1 - A_2| \]
Substituting the values we have:
\[ A_{\text{min}} = |3 - 9| = | -6 | = 6 \]

### Step 4: Calculate the Ratio of Maximum to Minimum Amplitude
Now, we can find the ratio of maximum amplitude to minimum amplitude:
\[ \text{Ratio} = \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{12}{6} \]
Simplifying this gives:
\[ \text{Ratio} = 2 \]

### Final Answer
The ratio of maximum amplitude to minimum amplitude is:
\[ \text{Ratio} = 2 \]

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