Question

A wave is represented by the equation $y=y_{0}sin[10\pi x-15\pi t+\left(\frac{\pi }{3}\right)]$ where x is in metres and t in seconds. The equation represents a travelling wave:

• A. in the positive direction with a velocity 1.5 m/s and wavelength 0.2 m.
• B. in the negative direction with a velocity 1.5 m/s and wavelength 0.2 m.
• C. in the positive direction with a velocity 2 m/s and wavelength 0.2 m
• D. in the negative direction with a velocity 2 m/s and wavelength 1.5 m

Answer 1

The correct option is A in the positive direction with a velocity 1.5 m/s and wavelength 0.2 m.

Negative sing with ‘$\omega$’ indicates that wave is propagating along positive x – axis.
$\lambda =\frac{2\pi }{k}=\frac{2\pi }{10\pi }=0.2m$
$Andv=\frac{\omega }{k}=\frac{15\pi }{10\pi }=1.5m/s$