Wave Optics

JEE Main level, single correct, medium

19 of 191

Question 19 of 191

Two coherent sources of sound, S1{S}_{1} and S2,{S}_{2}, produce sound waves of the same wavelength λ=1m\lambda =1m are in phase. S1{S}_{1} and S2{S}_{2} are placed 1.5m1.5m apart (see fig). A listener, located at LL, directly in front of S2{S}_{2}, finds that the intensity is at a minimum when he is 2m2m away from S2{S}_{2}. The listener moves away from S1{S}_{1}, keeping the distance from S2{S}_{2} fixed. The adjacent maximum of intensity is observed when the listener is at a distance dd from S1{S}_{1}. Then dd is :

Show answer and solution

Answer: (B) 5m5m

Given,
Two sources od same wavelength,
λ=1m\lambda =1m
Distance between two sources,
S1S2=1.5m{S}_{1}{S}_{2}=1.5m
Distance of listener from the source
S2{S}_{2}, S2L=2m{S}_{2}L=2m
Condition for minimum intensity, at
2m2m is
Path difference,
P.D.=(2n+1)λ2...(1)P.D.=(2n+1)\dfrac{\lambda }{2}...(1)
⇒P.D.=22+(1.5)2=(2n+1)λ2\Rightarrow P.D.=\sqrt{{2}^{2}+(1.5{)}^{2}}=(2n+1)\dfrac{\lambda }{2}
⇒2.5=(2n+1)λ2...(1)\Rightarrow 2.5=(2n+1)\dfrac{\lambda }{2}...(1)
Now, the path difference between the rays is so that the adjacent maxima is obtained,

P.D.=d−2=nλ...(2)P.D.=d-2=n\lambda ...(2)
The path difference between adjacent maxima and minima is
λ2\dfrac{\lambda }{2}, form equation (1) and (2) we get,
(d−2)−2.5=λ2...(3)(d-2)-2.5=\dfrac{\lambda }{2}...(3)
⇒d−2=2.5+12\Rightarrow d-2=2.5+\dfrac{1}{2}
⇒d=5m\Rightarrow d=5m

JEE Main question paper PDF

Open a shift to read the full paper on this page, or download it.

JEE Main 2025 Apr 2 Shift 1 question paper

Open Download PDF

Opening paper…

Explain it as a whiteboard videoStep-by-step, in Hinglish or English. Your first video needs no login.Solved it on paper but got it wrong?Upload a photo of your working. Mistake Doctor marks the exact line that broke.
See it move: Wave optics: YDSE, diffraction and polarisation simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Wave Optics (Interference of Light), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.