for A sinusoidal wave traveling in the negative x-direction and is described by the function y(x,t with the following parameters: ymax = 3 m, λ = 0.6 m, f = 100 Hz. (a) Write a proper expression for the function y(x, t) (b) Find all possible values of the phase shift , when y(0,0)=0 (c) Find the wave phase velocity

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for A sinusoidal wave traveling in the negative x-direction and is described by the function y(x,t)
with the following parameters: ymax = 3 m, 2=0.6 m, f = 100 Hz.
(a) Write a proper expression for the function y(x,t)
(b) Find all possible values of the phase shift when y(0,0)=0
(c) Find the wave phase velocity
Transcribed Image Text:for A sinusoidal wave traveling in the negative x-direction and is described by the function y(x,t) with the following parameters: ymax = 3 m, 2=0.6 m, f = 100 Hz. (a) Write a proper expression for the function y(x,t) (b) Find all possible values of the phase shift when y(0,0)=0 (c) Find the wave phase velocity
Expert Solution
Step 1

  Given parameters are:

  • Wave is traveling in the negative x-direction
  • The amplitude of the sine function, ymax=3m,
  • Wavelength, λ=0.6m
  • Frequency, f=100Hz

The wave function modeling a sinusoidal wave with the initial phase shift ϕ is given by:

yx,t=ymaxcoskx±ωt+ϕwhere wave number, k=2πλangular velocity, ω=2πfϕ is the initial phase of the wave functionThe temporal term ωt wheter it is positive or negative depends on the sign of the wave. Since  the wave is traveling in negative x-direction . So the plus sign will be used for this wave. Therefore,yx,t=ymaxcoskx+ωt+ϕ

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