Ratio of amplitude for two wave is 6:11 .Find the ratio of maximum amplitude to minimum amplitude.

Answer

To solve the problem of finding the ratio of maximum amplitude to minimum amplitude given the ratio of amplitudes of two waves, we can follow these steps:

### Step 1: Understand the Given Data
We are given the ratio of the amplitudes of two waves, which is:
\[ \frac{A_1}{A_2} = \frac{6}{11} \]
This means that if we let \(A_1 = 6k\) and \(A_2 = 11k\) for some constant \(k\), we can express the amplitudes in terms of \(k\).

### Step 2: Calculate Maximum Amplitude
The maximum amplitude (\(A_{max}\)) is the sum of the two amplitudes:
\[ A_{max} = A_1 + A_2 = 6k + 11k = 17k \]

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

### Step 4: Find the Ratio of Maximum Amplitude to Minimum Amplitude
Now, we can find the ratio of maximum amplitude to minimum amplitude:
\[ \frac{A_{max}}{A_{min}} = \frac{17k}{5k} = \frac{17}{5} \]

### Final Answer
Thus, the ratio of maximum amplitude to minimum amplitude is:
\[ \frac{A_{max}}{A_{min}} = \frac{17}{5} \]

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