A progressive wave is represented by the equation y=6sin4pi(40t+x) where x and y are m and t in s. Find amplitude,angular frequency,frequency,wave number,wavelength,velocity and direction of wave movement?

1 Answer
Oct 31, 2015

For any general wave in sinusoidal form
#y=Asin(kx-omega t+phi)#, the meanings of the symbols are as follows :
#A# = Amplitude
#k=2pi/lambda# = wave number, where #lambda# is wavelength.
#omega=2pif# = angular frequency, where #f=1/T# is frequency, and T is period.
#phi# = phase angle shift.

So in this case, #y=6sin(4pix-160pit)#
Amplitude #A= 6m#.
Angular frequency #omega=160pi rad//s#
Frequency #f=omega/(2pi)=80Hz#
Wave number #k=4pi m^(-1)#
Wavelength #lambda=(2pi)/k=0,5m#
Velocity #v=f lambda=40m//s#
Direction of wave movement is forward, perpendicular to direction of disturbance, ie transverse wave.
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