A wave is represented by the equation
`y = A sin (10 pi x + 15 pi t + pi//3)`
Where x is in metre and t is in second.
a wave travelling in the positive x-direction with a velocity of 1.5 m/s
a wave travelling in the negative x-direction with a velocity 1.5 m/s
a wave travelling in the negative x-direction with a wavelength of 0.2 m
a wave travelling in the positive x-direction with a wavelength 0.2 m

Options

A. a wave traveling in the positive x-direction with a velocity 1.5 m/s
B. a wave traveling in the negative x-direction with a velocity 1.5 m/s
C. a wave traveling in the negative x-direction having a wavelength 0.2 m
D. a wave traveling in the positive x-direction having a wavelength 0.2 m

Answer

B, D

Explanation

`y=A sin(10 pix+15pit+pi//3)`
The standard equation of a wave traveling in X-direction is `y=A sin[(2pi)/(lambda)(vt+x)+(phi)]`
Comparing it with the given equation we find
`(2piv)/(lambda)=15pi and (2pi)/(lambda)=10pi`
`lambda=1/5=0.2m therefore v=(15pi)/(2pi)xx1/5=1.5 m//s`