Superposition wave values problem

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SUMMARY

The discussion focuses on solving a problem involving the superposition of two wave pulses on a string, where one pulse is inverted. Both pulses travel at a speed of 1.0 m/s and have a height of 1 mm. The key task is to determine the resultant wave values at specific positions and times, particularly at x = 4.1 m for t = 1.0 s, 2.0 s, 2.5 s, 3.0 s, and 4.0 s. The participant expresses difficulty in applying the superposition principle and calculating the slope of the inverted pulse.

PREREQUISITES
  • Understanding of wave mechanics and the superposition principle
  • Ability to analyze wave pulse characteristics, including height and width
  • Familiarity with basic kinematics, specifically wave speed
  • Graph interpretation skills for visualizing wave behavior
NEXT STEPS
  • Study the superposition principle in wave mechanics
  • Learn how to calculate the slope of wave pulses from graphical data
  • Explore examples of wave interference patterns
  • Practice problems involving wave speed and resultant wave calculations
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Students studying wave mechanics, physics educators, and anyone interested in understanding wave interactions and superposition principles.

Nghi
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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. Assume that the superposition principle holds for these waves, and that the absolute value of the height of each pulse is 1 mm in the figure below. Determine the value of the resultant wave at x = 4.1 m at t = 1.0 s, 2.0 s, 2.5 s, 3.0 s, and 4.0 s.

superpositionwave.jpg


Homework Equations



None? o_o

The Attempt at a Solution



Sorry to bother everyone on the same day again, but everyone is just so helpful on this forum! :) This one makes my heart sad because I don't know how to find the slope of pulse 2, which is essentially a straight line. :(

The only solutions I didn't get were t = 2.0 s and 2.5 s. But I think if I understood how to do 2.0 s, then 2.5 would be manageable.

I understand the idea of superposition, but I don't know how to apply it, I guess. Ha ha. :'( My friend mentioned something about finding the slope of pulse 2 first, but I don't know how to do that. I think it's because I'm underthinking.
 
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The slope of pulse two may be found using the graph. You know the height and the width of the pulse.
 

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