Question

When a plane wave train transverses a medium, individual particles execute a periodic motion given by the equation $y=5\sin \frac{\pi }{4}\left(4t+\frac{x}{16}\right)$ where the lengths are expressed in centimeters and time in seconds. Find the phase difference (in degree) for two positions of the same particles which are occupied at a time interval $0.8s$ apart .

Answer 1

Answer: 144.00

Given equation of wave is,
$y=5\sin \frac{\pi }{4}\left(4t+\frac{x}{16}\right)$
$=5\sin \left(\pi t+\frac{\pi }{64}x\right)$
Here,
$v=\frac{\omega }{2\pi }=\frac{\pi }{2\pi }=\frac{1}{2}$
$T=\frac{1}{v}=2\sec$
$\Delta \varphi =\frac{2\pi }{T}(\Delta t)=\frac{2\pi }{2}(0.8)=0.8\pi$
$=0.8\times 3.14=2.512rad=144^{\circ }$