A wave equation which gives the displacement along the y-direction is given by `y = 10^(-4) sin(60t + 2x)` where `x and y` are in meters and `t` is time in seconds. This represents a wave

Options

A. travelling with a velocity of `30 m//s` in the negative x-direction.
B. of wavelength `pi m`
C. of frequency `30//pi Hz`
D. of amplitude `10^-4 m` travelling along the negative x-direction.

Answer

A, B, C, D

Explanation

`y = 10^(-4) sin (60 t + 2 x)`. Comparing the given equation with the stansard wave equation travelling in negative x-direction,
`y = a sin(omega t + kx)`
We get amplitude `a = 10^(-4) m`
Also `omega = 60`
`:. 2 pi f = 60 rArr f = (30)/(pi) Hz`
Also, `k = 2`
`rArr (2 pi)/(lamda) = 2 rArr lamda = pi m`
We know that
`v = f lamda = (30)/(pi) xx pi = 30 m//s`.