Good morning!
While I do prefer to show real demonstrations of physics concepts like we did last time
like this, wave interference via superposition is a topic where we should go over some idealized
multiple choice problems.
So, here goes! ♪flipping physics♪
Bo, please read and Bobby please answer the first problem.
- Two wave pulses on the same string are headed towards one another as shown.
When both occupy the same space, which diagram best describes the resulting waveform?
Wave pulses are shown with different colors to make them easier to visualize and talk about.
Does that mean the top illustration is all one rope even though it is black, red and blue?
- Yeah, if I made the whole illustration black, it would be more difficult to discuss and
visualize what happens.
Bobby?
- OK well, this is just interference via superposition like we did last time and you just demonstrated.
So, we draw both the red and blue waves in the middle at the same position and add their
amplitudes together...
The correct answer then has to be number one.
- I think it is also important to remember that after the two wave pulses interfere with
one another, they continue on with the same amplitude and direction as before, right?
Bobby and Billy you are both correct.
Bobby could you please read and Billy could you please answer the second problem.
- Two waves on the same string are headed towards one another as shown.
When the red wave occupies locations c and d and the blue wave occupies locations d and e,
which diagram best describes the resulting waveform?
Wave pulses are shown with different colors to make them easier to visualize and talk
about, again.
- OK, well, let's move the two waves to their respective locations and see what happens.
In locations d and e, the waves do not overlap so they do not interfere at all with one another,
so the answer could be 1, 2 or 4.
In location d, the two waves are mirror images of one another, so the two waves end up completely
canceling one another out in location d.
- That is total destructive interference.
- Right, so the correct answer is 2.
- Correct.
- But what happens when the two waves occupy the same space?
- Then the waves actually end up having the same exact shape in the same location and
we get constructive interference...
That means the resultant wave has twice the original amplitude as the two original waves.
- And after the two waves interfere with one another, they continue on with the same amplitude
and direction as before.
- Very nice y'all.
Okay, let's do one more problem.
Billy please read and Bo please answer the third problem.
- Two wave pulses on the same string are headed towards one another as shown.
When both occupy the same space, which diagram best describes the resulting wave form.
And then there's the same statement about the wave pulse colors.
- OK, so let's start by moving the two wave pulses to the middle where they overlap and
occupy the same space.
Well, that's not as easy as it was for the first two examples.
- You could start by looking at specific locations.
- Like the edges of the wave pulses.
- Sure, let's start with the left edge of the two pulses where the - - Call it location a.
It's always better to give things names.
- Fine, location a, the left edge of the two pulses where the red pulse is at its maximum
amplitude and the blue pulse is zero, when we add those together, we get the maximum
amplitude of the red pulse.
We can also look at the right edge of the two pulses...
Let's call it location b.
- Thanks.
- At location b, the red pulse is zero and the blue pulse is at its maximum amplitude
below equilibrium.
So, the result is the maximum amplitude of the blue wave below equilibrium.
That means the answer has to be either three or four because only three and four match
what we figured out about locations a and b.
- You're doing a great job Bo, please keep going.
- OK, well, let's pick another location...
How about right in the middle, we'll call it location c. At that point, the amplitudes
of the red and blue pulses are the same magnitude with the red above equilibrium and blue below
equilibrium, then the two waves cancel one another out right in the middle.
That means we know the answer - well, it's still 3 or 4 because both of those have zero
amplitude in the middle.
So we need to pick another location, let's say 1/4 of the way to the right of the left
edge, we'll call it location d. At that point, the red wave is 3/4 of the maximum amplitude
and above equilibrium and the blue wave is 1/4 of the maximum amplitude and below equilibrium.
Those two waves add up to half the maximum amplitude above equilibrium, therefore the
correct answer must be 4 because 4 is at half the maximum altitude above equilibrium 1/4
of the way to the right from the left edge, location d.
Choice 3 is less than half the maximum altitude at that point, so yeah, it has to be choice 4.
- And after the two waves interfere with one another, they continue on with the same amplitude
and direction as before.
- Really?
Again?
- Yes.
- Very nice everybody!
OK, so please, when you see questions like these, remember to determine how the amplitudes
add together because waves interfere with one another when they occupy the same space
via superposition the addition of the waves.
Thank you very much for learning with me today, I enjoyed learning with you!