Question

A wave disturbance in a medium is described by `y(x, t) = 0.02 cos(50pit + (pi)/(2))cos(10pix)` where `x and y` are in meter and `t` is in second`
A. A node occurs at `x = 0.15 m`
B. An antinode occurs at `x = 0.3 m`
C. The speed of wave is `5 m//s`
D. The wave length is `0.2 m`

Answer 1

Correct Answer - A::B::C::D
It is given that `y(x,t) = 0.02 cos (50 pi t + pi//2) cos (10 pi x)`
`~= A cos (omega t + (pi)/(2)) cos kx`
Node occurs when `kx = (pi)/(2),(3pi)/(2)`, etec
`rArr 10 pi r = (pi)/(2),(3pi)/(2)`
`rArr x = 0.05 m, 0.15 m` option (a)
Anitnode occurs when `kx=pi,2pi,3pi` etc.
`rArr 10 pix = pi, 2pi, 3pi` etc
`rArr x = 0.1 m, 0.02 m, 0.3 m` option (b)
Speed of the wave is given by
`v=(omega)/(k) =(50 pi)/(10 pi)=5 m//s` option (c)
Wavelength is given by
`lamda=(2 pi)/(k)=(2pi)/(10 pi) =((1)/(5))m=0.2 m`. option (d).