Question

The equation of a travelling wave is $y=0.07sin(12\pi x-500\pi t)$, where the distances are in meter and time t in second. Calculate the wavelength and velocity of the wave.

Answer 1

$y=0.07\sin (12\pi x-500\pi t)$

Compare it with standard equation

$y=A\sin (wt-kx)$

we get

$w=500\pi rad/sec$

and $k=12\pi$

As we know

$k=\frac{2\pi }{\lambda }\therefore \lambda =\frac{2\pi }{k}=\frac{2\pi }{12\pi }=\frac{1}{6}m$

Also

$w=2\pi f\therefore f=\frac{w}{2\pi }=\frac{500\pi }{2\pi }=250Hz=f\lambda =250\times \frac{1}{6}=41.67m/sec$