Question

Two waves of equal amplitude $x_0$ and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is

• A. $0$
• B. $x_0$
• C. $2x_0$
• D. Between $0$ and $2x_0$

Answer 1

The correct option is D Between $0$ and $2x_0$

The amplitude of the resultant wave is
$x_0^{\prime }=\sqrt{x_{01}^2+x_{02}^2+2x_{01}{x}_{02}\cos \left(\varphi \right)}$, here the angle between the two propagating waves is $\varphi$.
$x_0^{\prime }$ is maximum when $\varphi =0^o$ and it becomes $x_0^{\prime }=x_{01}+x_{02}=2x_0$ for $x_{01}=x_{02}=x_0$.
$x_0^{\prime }$ is minimum when $\varphi ={180}^o$ and it becomes $x_0^{\prime }=x_{01}-x_{02}=0$ for $x_{01}=x_{02}=x_0$.
The amplitude of the resultant wave is between 0 and 2$x_0$.