Good morning!
The last two lessons demonstrated standing wave patterns; however, it is important to
realize they were all created using transverse waves.
♪flipping physics♪
I thought it would be helpful to look at standing wave patterns created using longitudinal waves as well.
Billy, remind me of the difference between transverse and longitudinal waves.
- Whether a wave is transverse or longitudinal has to do with the direction of wave propagation
relative to the direction of the disturbance of the medium.
In a transverse wave, the direction of wave propagation is perpendicular to the direction
of the disturbance of the medium.
In a longitudinal wave, the two are parallel to one another.
- Right, so this is what four standing wave patterns look like for a longitudinal wave.
The oscillator is moving up and down at the shown number of cycles per second or Hertz
for each of the four springs.
Actually, just like before, it is difficult to see what is happening at real speed, so
let's slow it down to 32 times slower than real speed and also let's turn all the
videos horizontal so the springs are bigger on the screen.
- I still don't really see what is going on.
Could you add the video echo effect?
That was helpful last time.
- Yes, sure.
So, I can add that, however, I don't think it helps with understanding this time.
- No, that is not helpful.
- Yeah.
I still do not see what is going on.
- Maybe we should go back to that standing wave animation with the blue and red waves
constructively and destructively interfering to create the standing wave pattern.
- Good idea Bobby.
Bo, remind me of what the blue, red and black waves represent.
- The blue waves represent the periodic waves being created by the oscillator, and the red waves
represent the waves which are reflected at the end of the spring and headed back toward the oscillator.
The black wave represents the standing wave pattern which is created by the interference
of the blue and red waves and the black standing wave pattern is the only one we actually see.
- Perfect Bo.
So, let's remove the blue and red waves...
And Bobby, considering this is a longitudinal wave, what is on the y-axis of this animation?
- Well, when it was a transverse wave, position
was on the y-axis but this - this is a longitudinal wave.
- Its density.
- Oh, that's right.
Density is on the y-axis for a longitudinal wave.
Thanks Billy.
- You're welcome Bobby.
- Right, so the density of the wave will be increasing and decreasing according to the
pattern shown in the standing wave pattern.
Now, to understand what is going on in the longitudinal standing wave pattern, let's
bring back just the 33 Hz demonstration and adjust the location size and speed of the
black standing wave pattern animation to better align with of the 33 Hz demonstration.
Now do you see the longitudinal standing wave pattern?
- I see it.
- I do too.
- Yep, there it is.
- I mean really, you can see the locations where the density increases and decreases
the most.
- Those are the antinodes where the waves interfere to cause the largest amplitude.
- Oh, right.
And the locations of total destructive interference are the nodes.
- That means the nodes are where the density of the spring stays constant the whole time.
- Sure, nodes are where there's constant density but the nodes are more difficult to see than
the antinodes.
- The animation does help to show where the nodes are.
- That's true.
- I do want to look at what happens when I pause the video while the standing wave animation
is completely flat.
At this moment, the density of the entire spring should be the same and you can see
that it is pretty darn close to correct.
At this moment, the animation is completely flat which means the entire spring should
have a density which is at the equilibrium position which means the density is constant,
which is what you see in the spring.
Thank you very much for learning with me today, I enjoyed learning with you.
Actually you know what?
Sorry, but there is one more thing.
- Oh good.
- Oh, great.
- The original top animation has density on the y-axis...
However, we can also shift the animation over 1/4 cycle and have the animation illustrate
something different about the longitudinal standing wave pattern.
What do you think the bottom animation is showing now?
- Well, it looks like the spring does not change positions at each of the nodes.
- And the spring has its largest change in position at the anti-nodes.
- Oh!
So the bottom animation is showing displacement nodes and antinodes.
- Cool. - Correct.
The top animation is in terms of density and the bottom animation is in terms of displacement,
and you can see how each of the density nodes is a displacement anti-node and each of the
density anti-nodes is a displacement node.
That will be helpful to understand when we get to standing sound waves in musical instruments.
- Oh, that's going to be fun.
- Yes Billy, it will.
OK, I'm done now.
Thank you again for learning with me today, I enjoyed learning with you.