Question

Equation of two progressive waves are given by y1 = α sin [ωt + Φ1] and y2 = α sin [ ωt + Φ2] If amplitude and time period of resultant wave are same as that of both the waves,then (Φ1 -Φ2) is

a) π/3. b)2π/3. c) π/6. d)π/4​

Answer 1

Q]___

The given progression waves are

y1 = a sin (ωt +Φ1 )

y2 = a sin (ωt +Φ2 )

The resultant of two waves is

y = y1 + y2

y = a [ sin (ωt +Φ1) + sin (ωt +Φ2) ]

If A is the amplitude of the resultant wave,then

A = a ...[given]

∴ A^2 = a^2 + a^2 + 2a^2 cos Φ

or a^2 = a^2 + a^2 + 2a^2 cos Φ

or cos Φ = -1/2 = cos 120°

∴ Φ = 120°= 2π/ 3

Thus Φ1 -Φ2 = 2π /3

Option B.

Answer 2

Answer:

Option b) is the correct answer 2π/3

Hope it will be helpful ☺️ thank you!