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 $y(x, t)=8.0 \sin \left(0.5 \pi x-4 \pi t-\frac{\pi}{4}\right) \ldots$. (i)
The standard wave equation can be written as,
$y=a \sin (k x-\omega t+\phi)$...(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 $v=\frac{\omega}{k}$
$=\frac{4 \pi}{0.5 \pi}=8 \,m / s$