Ratio of amplitude for two wave is 1:3 .Find the ratio of maximum amplitude to minimum amplitude.

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Understand the Given Data
We are given the ratio of amplitudes of two waves, \( A_1 \) and \( A_2 \), as:
\[ \frac{A_1}{A_2} = \frac{1}{3} \]
From this, we can assign values to \( A_1 \) and \( A_2 \):
\[ A_1 = 1 \quad \text{and} \quad A_2 = 3 \]

### 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:
\[ A_{\text{max}} = 1 + 3 = 4 \]

### Step 3: Calculate Minimum Amplitude
The minimum amplitude \( A_{\text{min}} \) is calculated by subtracting the smaller amplitude from the larger one:
\[ A_{\text{min}} = A_2 - A_1 \]
Substituting the values:
\[ A_{\text{min}} = 3 - 1 = 2 \]

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

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

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