Question

A transverse wave propagating along x-axis is represented by $y(x,t)=8.0\sin (0.5\pi x-4\pi t-\pi /4)$ where x is in metres and t is in seconds. The speed of the wave is :-

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

Answer 1

Answer: (A)

$y(x,t)=8.0\sin \left(0.5\pi x-4\pi t-\frac{\pi }{4}\right)$
Compare with a standard wave equation,
$y=a\sin \left(\frac{2\pi x}{\lambda }-\frac{2\pi t}{T}+\varphi \right)$
we get $\frac{2\pi }{\lambda }=0.5\pi$
or, $\lambda =\frac{2\pi }{0.5\pi }=4m$.
$\frac{2\pi }{T}=4\pi$
or,$T=\frac{2\pi }{4\pi }=\frac{1}{2}\sec$
$v=1/T=2Hz$.
Wave velocity, $v=\lambda v=4\times 2=8m/\sec$.