Question

A transverse wave of amplitude $0.01m$ and frequency $500Hz$ is travelling along a stretched string with a speed of $200m/s$. Find the displacement of a particle at a distance of $0.7m$ from the origin after $0.01s$. Also find the phase difference between the point where wave reaches from the origin

Answer 1

Given: $a=0.01m$
$n=500Hz$
$v=200m/s$
$V=n\lambda$
$\lambda =\frac{V}{n}=\frac{200}{500}=0.4$
$y=a\sin \left(2\pi (\frac{t}{T}-\frac{x}{\lambda })\right)$
$=0.01\sin \left[2\pi (0.01\times 500-\frac{0.7}{0.4})\right]$
$=0.01\sin \left[2\pi \right(5-1.75\left)\right]$
$=0.01\sin [180\times \frac{13}{2}]=0.01\sin {1170}^{\circ }$
$=0.01\sin (3\times {360}^{\circ }+{90}^{\circ })=0.01\sin 90$
$y=0.01m$
$△\varphi =\frac{2\pi }{T}\times △t$
$=2\pi \times 500\times 0.01$
$△\varphi =10\pi$