The displacement of a particle in a medium can be expressed as
`y=10^(-6)sin(100t+20x+pi//4),`
where x is in metre and t is in second. What is the speed of the wave?

Options

A. `2000 ms^(-1)`
B. `5 ms^(-1)`
C. `20 ms^(-1)`
D. `5 pi ms^(-1)`

Answer

B

Explanation

The displacement is given by
`y=10^(-6) sin (100t+20x+pi/4)`
Comparing with standard equation
`y=a sin (omega t+kx+phi)`
`omega=100, k=20`
where, `omega` is angular frequency and k is angular wave number.
Now, `k=(2pi)/lambda=(2 pi v)/(lambda v)=omega/v=20`
`implies v=omega/20=100/20=5 ms^(-1)`
So, the speed of the wave is `5 ms^(-1)`.