Two wave of amplitude `A_(1)`, and `A_(2)` respectively and equal frequency travels towards same point. The amplitude of the resultant wave is

Options

A. `A_(1) + A_(2)`
B. `A_(1) - A_(2)`
C. between `A_(1) + A_(2)` and `A_(1) - A_(2)`
D. Can not say

Answer

To find the amplitude of the resultant wave when two waves of amplitudes \( A_1 \) and \( A_2 \) travel towards the same point, we need to consider the conditions of constructive and destructive interference.

### Step-by-Step Solution:

1. **Understanding Wave Interference**:
- When two waves meet, they can interfere constructively or destructively depending on their phase relationship.

2. **Constructive Interference**:
- If the two waves are in phase (constructive interference), the amplitudes add up.
- The resultant amplitude \( A_r \) can be expressed as:
\[ A_r = A_1 + A_2 \]

3. **Destructive Interference**:
- If the two waves are out of phase (destructive interference), the amplitudes subtract from each other.
- The resultant amplitude in this case can be expressed as:
\[ A_r = |A_1 - A_2| \]
- This means the resultant amplitude will be the absolute difference between the two amplitudes.

4. **Resultant Amplitude**:
- The resultant amplitude will depend on the phase difference between the two waves.
- Therefore, the resultant amplitude can vary between:
\[ A_r = A_1 + A_2 \quad \text{(maximum, constructive)} \]
and
\[ A_r = |A_1 - A_2| \quad \text{(minimum, destructive)} \]

5. **Conclusion**:
- The final resultant amplitude \( A_r \) lies between \( A_1 + A_2 \) and \( |A_1 - A_2| \), depending on the phase difference of the waves.