Question

A transverse wave propagating along x-axis is represented by $y(x,t)=8.0\sin \left(05\pi x-4\pi t-\frac{\pi }{4}\right)$ where $x$ is in metre and $t$ is in second. The speed of the wave is

• A. 4 $\pi$ m/s
• B. 0.5 $\pi$ m/s
• C. $\frac{\pi }{4}$ m/s
• D. 8 m/s

Answer 1

Answer: (D)

The given equation is $y(x,t)=8.0\sin \left(0.5\pi x-4\pi t-\frac{\pi }{4}\right)\dots$. (i)
The standard wave equation can be written as,
$y=a\sin (kx-\omega t+\varphi )$...(ii)
where $a$ is amplitude,
$k$ the propagation constant
and $\omega$ the angular frequency,
comparing the Eqs. (i) and (ii), we have
$k=0.5\pi ,\omega =4\pi$
$\therefore$ Speed of transverse wave $v=\frac{\omega }{k}$
$=\frac{4\pi }{0.5\pi }=8m/s$