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

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