Question

A wave is represented by the equation $y=Asin(10\pi x+15\pi t+\frac{\pi }{3})$ where x is in metre and t is in second. The expression represents

• A. a wave travelling in positive x-direction with a velocity 1.5 m/s
• B. a wave travelling in negative x-direction with a velocity1.5 m/s
• C. a wave travelling in the negative x-direction having a wavelength 0.4 m
• D. a wave travelling in positive x-direction of wavelength 0.1 m

Answer 1

The correct option is B a wave travelling in negative x-direction with a velocity1.5 m/s

$\omega =15\pi ,k=10\pi$
$v=\frac{\omega }{k}=1.5m/s$
$\lambda =\frac{2\pi }{k}=\frac{5\pi }{10\pi }=0.2m$
Positive sign between kx and $\omega$t means wave is travelling in negative x-direction.