Question

A certain transverse wave is described by
$y(x,t)=\left(6.50mm\right)cos2\pi (\frac{x}{28.0cm}-\frac{t}{0.0360s})$
The wave's speed of propagation is approximately (in m/s):

Answer 1

A right travelling transverse wave has form $y=Acos(kx-\omega t)$

where $A$ is the wavelength of the wave,

$k=\frac{2\pi }{\lambda }$, $\lambda$ is the wavelength

$\omega =2\pi \nu$, $\nu$ is the frequency of the wave

Thus wavelength of wave $\left(6.50mm\right)cos2\pi (\frac{x}{28.0cm}-\frac{t}{0.0360s})$

can be found by using $k=\frac{2\pi }{\lambda }$

$⟹\lambda =\frac{2\pi }{2\pi /28.0cm}=28.0cm$

Similarly frequency of wave can be found by $2\pi \nu =\frac{2\pi }{0.0360s}$

$⟹\nu =27.8Hz$

Speed of propagation=$\lambda \nu =7.8m/s$