Question

The wave function of a wave is given by the equation

D(x,t)=(0.2m)sin(2.0x−4.0t+π),

where x is in metres and t is in seconds.

a. What is the phase constant of the wave?

b. What is the phase of the wave at t=1.0s and x=0.5m?

c. At a given instant, what is the phase difference between two points that are 0.5m apart?

d. At what speed does a crest of the wave move?

Answer #1

from the given equation

D(x,t) = 0.2 sin (2x -4t + pi)

from the general equation

Y(x,t) = A sin (kx-wt + phi)

phase constant = phi = pi radians or 180 deg

-------------------------

part B:

at t= 1 and x = 0.5 s

D(x,t) = 0.2 sin (2* 0.5 -4*1 + pi)

D(x,t) = 0.2 sin (0+3.14)

phase = 0.14 radiains

------------------------

part C:

change of phase = 2* 0.5 - 4*0

Change of phase = 1 radians

--------------------------------

part :

max Speed Vmax = A W

Vmax = 0.2* 4

Vmax = 0.8 m/s

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