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) A node occurs at `x = 0.15 m`
B. (b) A antinode occurs at `x = 0.3 m`
C. ( c ) A speed wave is `5 ms^(-1)`
D. (d) A wave lengthis `0.3 m`

Answer 1

Correct Answer - C
( c ) Comaring it with
`y(x, t) = A cos(omegat + pi//2)coos k x`
If `k x = pi//2`, a node occurs,
:. `10pi x = pi//2 rArr x = 0.05m`
If `k x = pi`,an antinode occurs
rArr `10pix = pi rArr x = 0.1m`
aAlso speed of wave
`= (omega)/(k) = (50)/(10pi) = 5m//s` and `lambda = 2pi//k = 2pi//10pi = 0.2m`