Superposition wave values problem

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The discussion centers on a homework problem involving two wave pulses on a string, one of which is inverted. The pulses approach each other at a speed of 1.0 m/s, and the task is to determine the resultant wave at specific times and positions. The participant expresses confusion about applying the superposition principle and finding the slope of the inverted pulse. They mention needing help particularly with the calculations for times 2.0 s and 2.5 s. Understanding the slope of pulse two is identified as a key step in solving the problem.
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.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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