Question

The wave described by `y = 0.25 "sin"(10 pi x - 2pit)` , where x and y are in metres and t in seconds , is a wave travelling along the:
A. `+ ve` x direction with frequency 1 Hz and wavelength `lambda = 0.2 m`
B. `–ve` x direction with amplitude 0.25 m and wavelength `lambda = 0.2 m`
C. `– ve` x direction with frequency 1 Hz
D. `+ ve` x direction with frequency π Hz and wavelength `lambda= 0.2m`

Answer 1

Correct Answer - A
Given `y=0.25 sin (10pix-2pit)`
Comparing with equation of wave
`y=A sin (kx-omegat)`
`A=0.25, k=10pi, omega=2pi`
`(2pi)/(lambda)=10pi" "2pif=2pi`
`f=1Hz`
`lambda=(1)/(5)=0.2m`
When sign of coefficient of t and x are opposite it means `(dx)/(dt)=V gt 0` i.e., wave is propagating in the direction of growing x.