Two waves of the same frequency and same amplitude, on superimposition, produced a resultant disturbance of the same amplitude. The waves differ in phase by

Question

Two waves of the same frequency and same amplitude, on superimposition, produced a resultant disturbance of the same amplitude. The waves differ in phase by (A) π  (B) (2 π /3) (C) (π /2) (D) zero

Tardigrade Admin · Accepted Answer

Amplitude of resultant wave is A2=A12+A22+2A1A2cos θ Given, A=A1=A2=a (let) a2=a2+a2+2a2cos θ cos θ =-(1/2) θ =(2 π /3)

Q. Two waves of the same frequency and same amplitude, on superimposition, produced a resultant disturbance of the same amplitude. The waves differ in phase by

$π$

$\frac{2 π}{3}$

$\frac{π}{2}$

zero

Amplitude of resultant wave is
$A^{2} = A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos θ$

Given, $A = A_{1} = A_{2} = a$ (let)
$a^{2} = a^{2} + a^{2} + 2 a^{2} cos θ$
$cos θ = - \frac{1}{2}$
$θ = \frac{2 π}{3}$

Q. Two waves of the same frequency and same amplitude, on superimposition, produced a resultant disturbance of the same amplitude. The waves differ in phase by

π

32π​

2π​

zero

Amplitude of resultant wave is A2=A12​+A22​+2A1​A2​cosθ Given, A=A1​=A2​=a (let) a2=a2+a2+2a2cosθ cosθ=−21​ θ=32π​

$π$

$\frac{2 π}{3}$

$\frac{π}{2}$

Amplitude of resultant wave is
$A^{2} = A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos θ$

Given, $A = A_{1} = A_{2} = a$ (let)
$a^{2} = a^{2} + a^{2} + 2 a^{2} cos θ$
$cos θ = - \frac{1}{2}$
$θ = \frac{2 π}{3}$