Question

When a plane wave train transverses a medium, individual particles execute a periodic motion given by the equation $y=5 \sin \frac{\pi}{4}\left(4 t+\frac{x}{16}\right)$ 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 $0.8 \,s$ apart .

Answer 1

Given equation of wave is,
$y =5 \sin \frac{\pi}{4}\left(4 t+\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 \phi =\frac{2 \pi}{ T }(\Delta t )=\frac{2 \pi}{2}(0.8)=0.8 \pi $
$=0.8 \times 3.14=2.512 \,rad =144^{\circ}$