Question

When two sound waves travel in the same direction in a medium, the displacements of a particle located at ${}^{\prime }{x}^{\prime }$ at time ${}^{\prime }{t}^{\prime }$ is given by :
$y_1=0.05cos\left(0.50\pi x-100\pi t\right)$
$y_2=0.05cos\left(0.46\pi x-92\pi t\right)$
where $y_1,y_2$ and $x$ are in meters and $t$ in seconds. The speed of sound in the medium is :

• A. 92 m/s
• B. 200 m/s
• C. 100 m/s
• D. 332 m/s

Answer 1

Answer: (B)

Standard equation
$y\left(x,t\right)=Acos\left(\frac{\omega }{V}x-\omega t\right)$
From any of the displacement equation Say $y_1$
$\frac{\omega }{V}=0.05\pi and\omega =100\pi$
$\therefore \frac{100\pi }{V}=0.5\pi$
$\therefore V=\frac{100\pi }{0.5\pi }=200m/s$