# Waves and Superposition problem

• majormaaz
In summary, the two waves approach each other at the time t = 0, except that pulse 2 is inverted so that it is a downward deflection of the string rather than an upward deflection. The resultant wave at the times t = 1.0 s, 2.0 s, 2.5 s, 3.0 s, and 4.0 s is shown in the figure below. The superposition principle holds for these waves and the absolute value of the height of each pulse is 3 mm.
majormaaz

## 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?

majormaaz said:

## 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.
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.]

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!

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!

## 1. What is a wave?

A wave is a disturbance that travels through a medium, transferring energy from one point to another without the physical movement of the medium itself.

## 2. What is the superposition principle?

The superposition principle states that when two or more waves meet at a point, the resulting displacement is the algebraic sum of each individual wave's displacement at that point.

## 3. How do you calculate the resulting wave from two interfering waves?

To calculate the resulting wave from two interfering waves, you need to add their displacements at each point using the superposition principle. This will give you the amplitude and frequency of the resulting wave.

## 4. What is constructive interference?

Constructive interference occurs when two waves meet and their displacements are in the same direction, resulting in a larger amplitude. This can occur when waves are in phase, meaning their peaks and troughs align.

## 5. What is destructive interference?

Destructive interference occurs when two waves meet and their displacements are in opposite directions, resulting in a smaller or even zero amplitude. This can occur when waves are out of phase, meaning their peaks and troughs do not align.

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