Question

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

Answer 1

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