Consider a wave represented by `y=cos(500t-70x)` where y is in millimetres, x in metres and t in second. Which of following are true?

Options

A. The wave is a standing wave
B. the speed of the wave is `50//7 m//s`
C. The frequency of oscillation is `500xx2pi` Hz.
D. Two nearest points in the same phase have separation `20pi//7 cm`

Answer

b.,d.

Explanation

Comparing with `y=a cos(omegat-kx)`
`omega=500, k=70`
speed of wave
`=(omega)/(k)=(500)/(70)=(50)/(7)m//s`
`k=70`
`(2pi)/(lambda)=70`
or `lambda=(2pi)/(70)m=(2pi)/(70)xx100 cm=(20pi)/(7) cm`