Question

Two waves with same amplitude and frequency superpose at a point. The ratio of resultant intensities when they arrive in phase to that when they arrive $90^\circ$ out of phase is $\left[\cos \frac{\pi}{2} = 0\right]$

• A. $\sqrt{2}:1$
• B. $2:1$
• C. $4:1$
• D. $1:2$

Hint:

Intensity depends on phase difference due to the interference term.

Answer 1

The Correct Option is B

Step 1: Expression for resultant intensity.
\[ I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\phi \] Since amplitudes are same, $I_1 = I_2 = I_0$.

Step 2: Case 1 – Waves in phase.
\[ \phi = 0 \Rightarrow I = 4I_0 \]

Step 3: Case 2 – Waves $90^\circ$ out of phase.
\[ \phi = \frac{\pi}{2}, \cos\phi = 0 \] \[ I = 2I_0 \]

Step 4: Ratio of intensities.
\[ \frac{4I_0}{2I_0} = 2:1 \]

Step 5: Conclusion.
The required ratio is $2:1$.