Oscillations

JEE Main level, numerical answer, medium

186 of 194

Question 186 of 194

Two simple harmonic waves having equal amplitudes of 8cm8cm and equal frequency of 10Hz10Hz are moving along the same direction. The resultant amplitude is also 8cm8cm. The phase difference between the individual waves is _____ degree.

Show answer and solution

Answer: 120

If two waves have the same amplitude, frequency, and direction, but are out of phase by ϕ\phi degrees, then the amplitude of the resultant waves is given by AR=2Acos⁡(Δϕ2){A}_{R}=2A\cos \left(\dfrac{\Delta \phi }{2}\right)
Here, A1=A2=AR=8cm{A}_{1}={A}_{2}={A}_{R}=8cm
So, cos⁡(Δϕ2)=12\cos \left(\dfrac{\Delta \phi }{2}\right)=\dfrac{1}{2}
Or phase difference between the individual waves is Δϕ2=60∘⇒Δϕ=120∘\dfrac{\Delta \phi }{2}=60^{\circ}\Rightarrow \Delta \phi =120^{\circ}.

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: Simple pendulum simulationDrag the sliders and watch the numbers in this question change.

More Physics practice

JEE Main Physics practice question on Oscillations (Superposition of S.H.M's and Resonance), with the answer and a step-by-step solution. Scan a question from your own book or paper to get a whiteboard video.