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 1: Identify the amplitudes of the two waves
Let the amplitudes of the two waves be:
- Amplitude of the first wave, \( A_1 = a \)
- Amplitude of the second wave, \( A_2 = 2a \)

### Step 2: Understand the condition for constructive interference
In constructive interference, the waves are in phase, which means the phase difference \( \theta = 0 \) or \( \theta = 2n\pi \) (where \( n \) is an integer). This results in the maximum possible amplitude.

### Step 3: Use the formula for resultant amplitude
The resultant amplitude \( A_R \) when two waves interfere constructively is given by the sum of their amplitudes:
\[ A_R = A_1 + A_2 \]

### Step 4: Substitute the values of the amplitudes
Substituting the values of \( A_1 \) and \( A_2 \):
\[ A_R = a + 2a \]

### Step 5: Simplify the expression
Now, simplify the expression:
\[ A_R = 3a \]

### Conclusion
Thus, the resultant amplitude in the condition of constructive interference is \( 3a \).

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