Question

A harmonically moving transverse wave on a string has a maximum particle velocity and acceleration of $3m/s$ and $90m/s^2$ respectively. Velocity of the wave is $20m/s$. Find the waveform.

Answer 1

Maximum particle velocity,
$\omega A=3m/s...(i)$
Maximum particle acceleration,
${\omega }^{2}A=90m/s^2...(ii)$
Velocity of wave, $\frac{\omega }{k}=20m/s...(iii)$
From Eqs. (i), (ii) and (iii), we get
$\omega =30rad/s\Rightarrow A=0.1mandk=1.5m^{-1}$
$\therefore$ Equation of waveform should be
$y=A\sin (\omega t+kx+\varphi )$
$y=(0.1m)\sin [(30rad/s)t\pm ;(1.5m^{-1})x+\varphi ]$