A transverse wave propagating along x-axis is represented by: `y(x,t)=8.0sin(0.5pix-4pit-(pi)/(4))` Where `x` is in metres and `t` is in seconds. The speed of the wave is:

Options

A. 8 m/s
B. `4pi` m/s
C. `0.5pi` m/s
D. `(pi)/(4)` m/s

Answer

D

Explanation

`y(x,t)=8.0sin(0.5pix-4pit-(pi)/(4))`
Comparing it with standard wave equation
`y=asin((2pix)/(lambda)-(2pit)/(T)-phi)`, we get
`(2pi)/(lambda)=0.5pi or lambda=(2)/(0.5)=4m`
and `(2pi)/(T)=4pi or T=(2)/(4)=0.5s`
Speed of wave, `v=upsilonlambda=(lambda)/(T)=(4)/(0.5)=8m//s`