The periodic waves of amplitude 5 m and 2m respectively, pass together through a region. The difference in the maximum and the minimum resultant amplitude possible is

Options

A. 5 m
B. 2 m
C. 4 m
D. 1 m

Answer

To solve the problem of finding the difference in the maximum and minimum resultant amplitude of two periodic waves with given amplitudes, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amplitudes**:
- Let the amplitude of the first wave, \( A_1 = 5 \, \text{m} \).
- Let the amplitude of the second wave, \( A_2 = 2 \, \text{m} \).

2. **Determine Maximum Resultant Amplitude**:
- The maximum resultant amplitude occurs when the two waves are in phase (i.e., when their peaks align).
- This can be calculated as:
\[ A_{\text{max}} = A_1 + A_2 = 5 \, \text{m} + 2 \, \text{m} = 7 \, \text{m} \]

3. **Determine Minimum Resultant Amplitude**:
- The minimum resultant amplitude occurs when the two waves are out of phase (i.e., when one wave's peak aligns with the other's trough).
- This can be calculated as:
\[ A_{\text{min}} = |A_1 - A_2| = |5 \, \text{m} - 2 \, \text{m}| = 3 \, \text{m} \]

4. **Calculate the Difference**:
- Now, we find the difference between the maximum and minimum resultant amplitudes:
\[ \text{Difference} = A_{\text{max}} - A_{\text{min}} = 7 \, \text{m} - 3 \, \text{m} = 4 \, \text{m} \]

5. **Final Answer**:
- The difference in the maximum and minimum resultant amplitude possible is \( 4 \, \text{m} \).