The amplitude of two interfering waves are a and 2a respectively. The resultant amplitude in the condition of constructive interference will be:

Options

A. a
B. 2a
C. 3a
D. 5a

Answer

To solve the problem of finding the resultant amplitude of two interfering waves with amplitudes \( a \) and \( 2a \) under the condition of constructive interference, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Amplitudes**:
- Let the amplitude of the first wave be \( A_1 = a \).
- Let the amplitude of the second wave be \( A_2 = 2a \).

2. **Constructive Interference Condition**:
- In constructive interference, the two waves are in phase. This means that the phase difference \( \theta = 0 \), and hence \( \cos \theta = 1 \).

3. **Resultant Amplitude Formula**:
- The resultant amplitude \( A_R \) for two waves is given by the formula:
\[ A_R = A_1 + A_2 \]
- Since we are considering constructive interference, we can directly add the amplitudes.

4. **Calculate the Resultant Amplitude**:
- Substitute the values of \( A_1 \) and \( A_2 \):
\[ A_R = a + 2a = 3a \]

5. **Final Result**:
- Therefore, the resultant amplitude in the condition of constructive interference is:
\[ A_R = 3a \]