A wave equation which gives the displacement along y -direction is given by `y=0.001 sin (100t +x)` where x and y are in meterand t is time in second. This represented a wave

Options

A. of wavelength one metre
B. travelling with a velocity of 100 m/s in the negative X-direction
C. of frequency `(100)/(pi)Hz`
D. travelling with a velocity of `(50)/(pi)m//s` in the positive X-direction

Answer

B

Explanation

The +ve sign between x and t terms shows that the wave is travelling in the -ve X direction
Comparing `y = 0.001 sin (100 t + x)` with
`y = a sin (omega t + Kx)`, we get
`omega = 100 and K = 1 and a = 0.001 m`
`: n = (omega)/(2pi ) = (100)/(2pi) = (50)/(pi) Hz`
Velocity `v = (omega)/(K) = 100 m//s`
and `K = (2pi)/(lamda) :. lamda = (2pi)/(K) = 2pi m`
Thus if it represents a wave travelling with a velocity of 100 m/s in the -ve X-direction