Question

A wave travelling along a string is described by,
$y(x,t)=0.005sin(80.0x-3.0t)$, in which the numerical constants are in SI units (0.005 m, 80.0 rad $m^{-1}$ and 3.0 rad $s^{-1}$). Calculate :

(a) the amplitude
(b) the wavelength
(c) the period and frequency of the wave.
Also, calculate the displacement y of the wave at a distance x = 30.0 cm and time t = 20 s?

Answer 1

We know that

general equation of wave

$y(x,t)=A\sin (kx-\omega t)$

comparing this equation with given equation

$1)$ $A=0.005$m $\to$ amplitude

$k=80$

$\omega =3$

$2)$ $\lambda =\frac{2\pi }{k}=\frac{2\pi }{80}=\left(\frac{\pi }{40}\right)$m

$3)$ Time period $T=\frac{2\pi }{\omega }=\frac{2\pi }{3}$ sec

frequency $f=\frac{1}{T}=\frac{3}{2\pi }$Hz

$4)$ Displacement at $x=0.3$m

$t=20$ sec

$y=0.005\sin (80\times 0.3-3\times 20)$

$=0.005\sin (24-60)=0.005\sin (-36)$

$=0.00495$m

$y=4.9$mm.