Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the 3 times of amplitude of indiv

Question

Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the 3 ​ times of amplitude of individual motions. The phase difference between the two motions is

TestHub · Accepted Answer

Let the amplitude of the individual waves be $A$ and the phase difference be $ϕ$ .

The resultant amplitude $A_{R}$ of two superimposed waves is given by:

$A_{R} = A^{2} + A^{2} + 2 A^{2} cos ϕ$

Given that $A_{R} = 3 A$ , we have:

$3 A = 2 A^{2} + 2 A^{2} cos ϕ$

Squaring both sides:

$3 A^{2} = 2 A^{2} (1 + cos ϕ)$

$1 + cos ϕ = \frac{3}{2}$

$cos ϕ = \frac{1}{2}$

$ϕ = 6 0^{\circ}$

Answer: $6 0^{\circ}$

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