Ratio of amplitude for two wave is 1:4 .Find the ratio of maximum amplitude to minimum amplitude.

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the Given Information
We are given the ratio of the amplitudes of two waves, \( A_1 \) and \( A_2 \), which is \( 1:4 \). This means we can express the amplitudes as:
- \( A_1 = 1k \)
- \( A_2 = 4k \)
where \( k \) is a constant.

### Step 2: Calculate Maximum Amplitude
The maximum amplitude \( A_{\text{max}} \) is calculated by adding the two amplitudes together:
\[ A_{\text{max}} = A_1 + A_2 = 1k + 4k = 5k \]

### Step 3: Calculate Minimum Amplitude
The minimum amplitude \( A_{\text{min}} \) is calculated by taking the absolute difference of the two amplitudes:
\[ A_{\text{min}} = |A_1 - A_2| = |1k - 4k| = | -3k | = 3k \]

### 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:
\[ \text{Ratio} = \frac{A_{\text{max}}}{A_{\text{min}}} = \frac{5k}{3k} = \frac{5}{3} \]

### Final Answer
The ratio of the maximum amplitude to the minimum amplitude is \( \frac{5}{3} \).

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