Question

In the given progressive wave `y=5sin (100pit-0.4pix)` where y and x are in m, t in s, what is the (a) amplitude (b) wavelength (c) frequency (d) wave velocity (e) particle velocity amplitude.

Answer 1

The given equation is `y=5sin(100pit-0.4pix)`
Compart is with the standard form of eqn. of progressive wave `:y=rsin[(2pit)/(T)-(2pi)/(lambda)x]`
(a) amplitude, `r=5m` (b) `(2pi)/(lambda)=0.4pi, lambda=(2pi)/(0.4pi)=5m`
(c) `(2pi)/(T)=100pi, (1)/(T)=v=(100pi)/(2pi)=50Hz` (d) wave velocity, `upsilon=vlambda=50xx5=250m//s`
(e) particle velocity, `(dy)/(dt)=5xx100picos(100pit-0.4pix)`
`((dy)/(dt))_(max)=500pixx1m//s=500pim//s`