Question

A wave travelling in positive X - direction with A = 0.2 m has a velocity of 360 m/s . If $\lambda =60m$ then the correct expression for the wave is :

Answer 1

Given,

Amplitude, $a=0.2m$

Velocity, $v=360m/s$

Wavelength, $\lambda =60m$

Equation of wave along x-axis is $y=a\sin (kx-\omega t)$

$k=\frac{2\pi }{\lambda }$

$k=\frac{2\pi }{60}=\frac{\pi }{30}$

$\because \omega =\frac{2\pi }{T}$

$and$

$v=\nu \lambda$

$\nu =\frac{v}{\lambda }=\frac{360}{60}=6Hz$

$so,$

$\omega =2\pi \times 6$

$\omega =12\pi$

So, equation of wave is $y=0.2\sin (\frac{\pi x}{30}-12\pi t)$