Question 101: Waves

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 $$\sqrt3$$ times of amplitude of individual motions. The phase difference between the two motions is ___________ (degree).

Accepted Answer

$${A_{net}} = \sqrt {A_1^2 + A_2^2 + 2{A_1}{A_2}\cos \phi } $$
$$\sqrt 3 A = \sqrt {{A^2} + {A^2} + 2{A^2}\cos \phi } $$
$$3{A^2} = 2{A^2} + 2{A^2}\cos \phi $$
$$\cos \phi  = {1 \over 2}$$
$$\phi  = 60^\circ $$

Waves

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 $\sqrt3$ times of amplitude of individual motions. The phase difference between the two motions is ___________ (degree).

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