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Waves and Superposition problem

  • Thread starter majormaaz
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  • #1
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Homework Statement



Two wave pulses on a string approach one another at the time t = 0, as shown in the figure below, except that pulse 2 is inverted so that it is a downward deflection of the string rather than an upward deflection. Each pulse moves with a speed of 1.0 m/s. Make a careful sketch of the resultant wave at the times t = 1.0 s, 2.0 s, 2.5 s, 3.0 s, and 4.0 s, assuming that the superposition principle holds for these waves, and that the absolute value of the height of each pulse is 3 mm in the figure below.

Picture found at http://www.cramster.com/answers-jan-08/physics/wave-pulses-string-approach-time_167341.aspx?rec=0

Homework Equations


Superposition - adding up the amplitudes,


The Attempt at a Solution


I understand that at t = 1.0 and 4.0 seconds, the superposition would be 0, and why t = 3.0 seconds would be the amplitude, 3mm, but I don't know how to find t = 2 and 2.5 seconds. I'm think that if they were simple sine waves, I could just add them, but they are different shapes. Would that affect the amplitude?
 

Answers and Replies

  • #2
collinsmark
Homework Helper
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Homework Statement



Two wave pulses on a string approach one another at the time t = 0, as shown in the figure below, except that pulse 2 is inverted so that it is a downward deflection of the string rather than an upward deflection. Each pulse moves with a speed of 1.0 m/s. Make a careful sketch of the resultant wave at the times t = 1.0 s, 2.0 s, 2.5 s, 3.0 s, and 4.0 s, assuming that the superposition principle holds for these waves, and that the absolute value of the height of each pulse is 3 mm in the figure below.

Picture found at http://www.cramster.com/answers-jan-08/physics/wave-pulses-string-approach-time_167341.aspx?rec=0

Homework Equations


Superposition - adding up the amplitudes,


The Attempt at a Solution


I understand that at t = 1.0 and 4.0 seconds, the superposition would be 0, and why t = 3.0 seconds would be the amplitude, 3mm,
Okay, so far so good. :approve:
but I don't know how to find t = 2 and 2.5 seconds. I'm think that if they were simple sine waves, I could just add them, but they are different shapes. Would that affect the amplitude?
If the superposition principle holds, you can ad them together regardless of their shape. The essence of the superposition principle means that you can add individual contributions together to obtain the final result. The problem statement said, "...assuming that the superposition principle holds for these waves..." So you can add them together.

[If you're curious, Fourier decomposition/analysis is based on the superposition principle using sinusoidal waves. But the superposition principle is not limited to sinusoidal waves. Examples applications of the superposition principle for non-sinusoidal waveforms include wavelet transformations, the Hilbert space of Quantum mechanics, most all modern digital communication systems (cell phones, WiFi, etc.) among other things.]
 
  • #3
62
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ok, thanks! I realized that I actually had to draw the problem out frame by frame to get the 2 and 2.5 secs answer. Thanks! :approve:

Just for those who might stumble on this thread, what you have to do is look at the x value they give you, then subtract it from the nearest whole number. For example, I had 4.2. I did 4.2 - 4 to get 0.2 This is the point where we have to see what the superposition is. If you draw it out, Only the valley-shaped pulse is there. You can set a proportion of the pulse's height / 0.5(half the total base) to the height of the amp (0.2 relative to 4) / 0.2.

2.5 is just part(c) * -1
Thanks again, collinsmark!
 

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