Ratio of amplitude for two wave is 8:4 .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 as 8:4, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
We are given the ratio of the amplitudes of two waves, A1 and A2, as:
\[ \frac{A1}{A2} = \frac{8}{4} \]
This implies that \( A1 = 8k \) and \( A2 = 4k \) for some constant \( k \).

2. **Calculate Maximum Amplitude (Amax)**:
The maximum amplitude when two waves interfere constructively is given by the sum of their amplitudes:
\[ A_{max} = A1 + A2 \]
Substituting the values of A1 and A2:
\[ A_{max} = 8k + 4k = 12k \]

3. **Calculate Minimum Amplitude (Amin)**:
The minimum amplitude when two waves interfere destructively is given by the absolute difference of their amplitudes:
\[ A_{min} = |A1 - A2| \]
Substituting the values of A1 and A2:
\[ A_{min} = |8k - 4k| = 4k \]

4. **Find the Ratio of Maximum Amplitude to Minimum Amplitude**:
Now, we can find the ratio of maximum amplitude to minimum amplitude:
\[ \frac{A_{max}}{A_{min}} = \frac{12k}{4k} \]
Simplifying this gives:
\[ \frac{A_{max}}{A_{min}} = \frac{12}{4} = 3 \]

### Final Answer:
The ratio of maximum amplitude to minimum amplitude is \( 3:1 \).

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