- Good morning.
♪flipping physics♪
Resonance involves a standing wave patterns.
So, if you have not learned about standing waves, please enjoy my video about standing wave patterns.
Link is in the description.
Here we go!
As I slide my fingers across this aluminum rod, the friction between my hand and the
rod causes vibrations which set up a standing wave pattern in the rod because the rod has
a resonance frequency and resonance wavelength determined by the physical characteristics of the rod.
Because I am holding the rod in the center of the rod, that forces the center of the rod to not vibrate.
Bo, in terms of nodes and antinodes, what do you think that means for the movement of the rod?
- OK.
The location you hold the rod at forces the rod to not vibrate there, so that must be a node.
I'm guessing then that the two ends of the rod probably vibrate the most which would
make the two ends antinodes.
- Correct.
So, you can hear that standing waves are happening in this rod.
In other words, this rod is resonating which is why this frequency you hear is called the
"Resonance Frequency" of the rod.
Another term often used is that this is the "Natural Frequency" of the rod.
In other words, the friction between my fingers and the rod oscillate the rod at the resonance
frequency of the rod causing standing wave patterns in the rod which is called "Resonance".
- I'm sorry, what?
- I don't get it.
- OK, let's switch to a simpler example.
This is a swing which is a pendulum.
A pendulum has a natural frequency at which it oscillates.
If I apply a force to the pendulum at a frequency which matches the natural or resonance frequency
of the pendulum, the amplitude of the pendulum will increase.
The pendulum will be resonating due to my force applied at the natural frequency of the pendulum.
If instead I apply a force to the pendulum which is at a frequency which does not match
the natural frequency of the pendulum, the amplitude of the pendulum will not increase.
- Sure..
Applying a force at a frequency which closely matches the resonance frequency of the object
will set up standing wave patterns in the object which is called "Resonance".
- Correct Billy.
We can do the same thing we did with the aluminum rod with a goblet.
By running my damp finger over the top of this goblet, I set up a standing wave pattern
in the Goblet at its resonance frequency which you can clearly hear.
When I change the amount of water in the goblet, I can change the natural or resonance frequency
of the goblet.
You can even see that the vibrations of the goblet cause ripples in the water.
A hollow tube has air in it which will also resonate at particular frequencies, which
is why, if I hold an oscillating tuning fork over a hollow tube with one end in water,
I can adjust the length of the hollow tube which is filled with air therefore changing
the resonance frequency of the air column inside the tube until it matches the frequency
of the tuning fork and when the frequency of the tuning fork matches the resonance frequency
of the air column inside the hollow tube, you can hear the louder standing wave pattern
which has been established in the air column inside the hollow tube.
When I change the frequency of the tuning fork, you can see it changes the length of
the tube which is out of the water in which the standing wave pattern is created and therefore
changes the resonance frequency of the air column in the hollow tube.
We can even take a very long, hollow tube and adjust the frequency of the sound being played
into the hollow tube and find the resonance frequency of this long hollow tube which is 68 Hz.
At this frequency, a standing wave pattern is created in the air inside the tube and
you can even feel the air oscillating at the end of the tube.
- Maybe you can feel it but we can't.
- Oh right.
So, I'll put a soap bubble in the end of the tube so you can see how the oscillating air
vibrates the bubble.
- Thanks Mr. P. That's much better.
- Actually, I cannot resist showing you slow-motion of the bubble vibrating due to the oscillating
air at the end of the hollow tube...
I love this!
- Me too.
- Is this how musical instruments work?
- Good point Bobby...
Wind instruments are instruments which create a pitch by vibrating a column of air inside the instrument.
Examples of this would be horns, flutes, clarinets, penny whistles and so forth.
So yes, wind instruments create music by creating resonance waves or standing waves in the air
column inside the instrument.
In fact, this is exactly what you hear when you hold a large seashell to your ear.
What you are hearing is various frequencies from the ambient noise setting up standing
waves in the seashell at resonance frequencies for the air columns inside the seashell.
And the frequencies which do not match the resonance frequencies in the air column in
the seashell are dampened.
That results in an echoey sound some people call "The sound of the Sea".
This speaker which is from a pair of speakers I purchased in college has resonance frequencies
at low frequencies which you can hear as I adjust the frequency of the sound being played by the speaker.
- That is a terrible idea.
Why would someone design a speaker with resonance frequencies?
- Correct it would be a terrible idea.
What happened to this speaker is that I dropped the speaker too many times while moving in college.
Evidently, dropping a speaker is not good for it.
You can also hear the standing waves are not created in the speaker at higher frequencies.
One of my favorite practical examples of resonance frequency is resonance frequency of the human body.
So what I have is a key fob and a human body and what I can do is I can take the key fob
and I can hold it right here and I can press the button...
And what's going on here is the key fob sends out a radio wave, and that radio wave should
reach my vehicle, the Flipping Physics vehicle in the back, but it does not - I'm just a
little bit too far for that to work.
So what I can do instead is I can hold the key fob right here...
And what you can see is it now is able to reach the car.
So what's going on is the frequency and wavelength of the key fob matches a resonance frequency
and wavelength of my body and therefore sets up a standing wave pattern in my body which
amplifies the signal and makes it so the radio waves can reach the car to lock and unlock the car.
- Mr. P, can we go back to the original singing rod demonstration?
- Sure Bobby...
If your fingers are in the middle of the rod causing a node and the ends of the rods are
antinotes, that means the length of the rod is half the wavelength of the sound wave.
- And if we measure the length of the rod, we can double it to determine the wavelength
of the resonance wave setup in the rod.
- Even better, if we can measure the frequency emitted by the rod, we can determine the speed
of the wave in the rod using the equation speed equals frequency times wave length.
- The length of the rod is 0.750m and frequency analysis of the sound says the frequency is
3310 Hz. Have at it!
- Then the wave length of the wave in the standing wave pattern in this rod is two times
the length of the rod or 1.5m.
Speed equals frequency times wavelength means that the speed of the wave in this rod is
3,310 times 1.5 or 4,965 - well, with three sig figs 4,960 meters per second.
- Wow!
Just so you know, according to EngineeringToolBox.com,
the speed of a wave in an aluminum rod like
this is 5,000 meters per second. So our predicted wave speed is very close to the published wave speed.
- Wow!
- Cool.
- But what happens to the frequency if I do the same thing with a shorter aluminum rod?
Let's say one which is 0.500m long?
- Well, the situation is the same as before; however, the length of the rod is decreased.
So, because wavelength and frequency are inversely related, the frequency of the standing wave
should be increased, we should hear a higher pitch.
- And we can actually determine the frequency. There is still one node in the middle
and two antinodes on the ends, so the length of the rod is still half a wavelength, that
means the wavelength equals two times the length of the rod so the wavelength equals one meter.
We measured the speed of the wave in an aluminum rod to be 4,960 m/s and the frequency equals
speed divided by wavelength or 4,960 over 1, therefore the frequency emitted by the shorter aluminum
rod should be 4,960 Hz.
- OK, let's test that.
You can clearly hear the pitch is increased in the shorter rod and my analysis of the
audio gives an average frequency of 4,960 Hz.
I think we can definitely say...
The physics works...
The physics works!
- Uh-huh uh-huh.
- The physics works.
Thank you very much for learning with me today, I enjoyed learning with you.