Two waves having equation x1=a sin (ω t-k x+φ1) x2=a sin (ω t-k x+φ2) If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is

Question

Two waves having equation x1=a sin (ω t-k x+φ1) x2=a sin (ω t-k x+φ2) If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is (A) (π/6) (B) (2π/3) (C) (π/4) (D) (π/3)

Tardigrade Admin · Accepted Answer

Resultant amplitude =2 a(1+ cos φ)= a ∴(1+ cos φ)=1 / 2 ; cos φ=-(1/2) ; φ=(2 π/3) text .

Q. Two waves having equation
$x_{1} = a sin (ω t - k x + ϕ_{1})$
$x_{2} = a sin (ω t - k x + ϕ_{2})$
If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is

$\frac{π}{6}$

$\frac{2 π}{3}$

$\frac{π}{4}$

$\frac{π}{3}$

Resultant amplitude $= 2 a (1 + cos ϕ) = a$
$∴ (1 + cos ϕ) = 1/2; cos ϕ = - \frac{1}{2}; ϕ = \frac{2 π}{3} .$

Q. Two waves having equation x1​=asin(ωt−kx+ϕ1​) x2​=asin(ωt−kx+ϕ2​) If in the resultant wave the frequency and amplitude remain equal to amplitude of superimposing waves, the phase difference between them is

6π​

32π​

4π​

3π​