The equation of a wave disturbance is given as `y=0.02cos((pi)/(2)+50pit) cos(10pix)`, where x an y are in metre and t in second. Choose the wrong statement.

Options

A. A node occurs at x=0.15 m
B. an antidone occurs at x=0.3 m
C. the speed of wave is 5m/s
D. the wave length of 0.2 m

Answer

A, B, C, D

Explanation

It is given that `y=(x,t)=0.02cos(50pit+pi//2)cos(10pix)congA cos(omegat+(pi)/2)cos kx`
Node occurs when `kx=(pi)/2,(3pi)/2,etc. implies 10pix=(pi)/2,(3pi)/3 implies x=0.05,-0.15m`
Antidode occurs when `kx=pi,2pi,3pi etc.implies 10pix=pi,2pi,3pi etc`.
`implies x=0.1 m,0.02m,0.3m ` option (B)
speed of the wave is given by `v=(omega)/k=(50pi)/(10pi)=5m//s` option (C)
Wavelength is given by `lambda=(2pi)/k=(2pi)/(10pi)=((1)/(5))m=0.2m` option(D)