Two sound waves each of wavelength $λ$ and same amplitude $A$ interfere at point $Q$. If the path difference is $\frac{λ}{4}$, the amplitude of the resultant wave at point $Q$ is $[sin\frac{π}{2} = 1,cos\frac{π}{2} = 0]$

Question

Assertion (A): When two waves of equal amplitude and a phase difference of $ \frac{\pi}{2} $ interfere, the resulting intensity is equal to the intensity of one wave. Reason (R): In interference, the resultant intensity is always the sum of individual intensities if the phase difference is non-zero.

Answer 1

Step 1: Approach
Add the two waves as perpendicular phasors.

Step 2: Phasors
A phase difference of $\pi/2$ means the phasors are at a right angle. Their resultant has length $\sqrt{A^2+A^2}=\sqrt2A$.

Step 3: Answer
Option (B). It lies between the minimum 0 and the maximum $2A$, as it should.

Final Answer:
The phase difference is pi/2, so the amplitude is root 2 times A, option (B). \[ \boxed{\sqrt2A} \]

Two sound waves each of wavelength \(λ\) and same amplitude \(A\) interfere at point \(Q\). If the path difference is \(\frac{λ}{4}\), the amplitude of the resultant wave at point \(Q\) is \([sin\frac{π}{2} = 1,cos\frac{π}{2} = 0]\)

Show Hint

The Correct Option is B

Solution and Explanation

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