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Old Aug 17th 2016, 07:22 AM   #1
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Waves and wave combination

I am finding wave equation questions quite difficult and was hoping for some help with these particular questions.

Q1: The figure on the left below shows the displacements of the particles in a string as a function of the position x along the string at t = 0. The figure on the right shows the displacement of the particle at x = 0m as a function of time.
The particle positions are measured from the left end of the spring (x = 0m) and the wave pulses move to the right.
Give the general representation of this motion in the standard form
y = Asin(kx - wt) where y is the wave disturbance. What form would the representation have if the wave was moving to the left?

Q2: Two sound waves with identical amplitudes but slightly different frequency emerge from a pair of speakers placed side by side. The frequency of the first is 2001 Hz and the frequency of the second source is 1999 Hz. By considering the time dependence only, obtain an expression for the form of the resulting wave explaining its significance. What phenomenon does this represent?
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Old Aug 17th 2016, 07:58 AM   #2
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I'll help you get started. From the standard equation for the particle at x = 0 its motion would be:

y(t, x=0) = A sin(wt)

Now look at the graph on the right - the period of motion (the time it takes to complete one cycle) is T=0.45 seconds. Recall that T = 2 pi/w, so from that you can calculate the value for w. The value for A is the amplitude of the wave, which you can read off the y-axis of the right hand graph. So now all that's left is the value for k. Consider what happens at t=0; per the standard equation the left hand graph is y(x, t=0) = A sin(kx). Looking at the length of one cycle it appears to be 0.02 meters, hence when x = 0.02, kx = 2 pi. Thus k = 2 pi/0.02m.
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Old Aug 17th 2016, 08:27 AM   #3
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You are a champ Chip
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