1. Standing Waves

2. Waves Review What is the definition of a wave?
A disturbance that carries energy
without transferring matter
What is the definition of a wave?
Example: Sound from a speaker traveling through air to my ear.
All waves ‘travel’ or carry energy from one location to another until the wave encounters some sort of barrier or new medium.
What happens then?
Depending on the barrier / new medium, some of the wave energy may transmit through. But some of the wave energy will be reflected.

3. Waves on a string
A great example of wave reflection and the interesting patterns that result from it are waves on a string/slinky. Because the string has a short length, the wave quickly runs into a barrier and reflects backward. .
Slinky Demo!
What would happen if I increased the rate of the pulses?
The original and reflected waves would interfere, creating odd patterns.
Are the original and reflected waves still traveling through the medium?
Yes! It just doesn’t look like it because we see the sum of their behavior.
We get the same behavior when a wave just reflects off a denser /slower speed medium.
Example: Rope attached to a fixed point. A wave pulse travels to the end and reflects back.

4. Standing Waves
If we vibrate the string at exactly the right frequency, we can create standing waves. Standing waves have points – called nodes – that appear to ‘stand still’. Standing waves result from the interference of two identical waves with the same frequency and the same amplitude traveling in opposite direction – such as we get with reflected waves (of certain frequencies) along a string. .
Antinode – maximal displacement
Do Slinky Demo!
node –zero displacement

5. Harmonics
Slinky Demo!
By adjusting the frequency of disturbance, standing waves of different wavelengths can be generated. The production of standing waves is how tones are generated in most instruments (strings, winds, brass, etc.)! .
Fundamental tone (first harmonic)
Show with slinky, show with demo –
Show on violin –
If I bow a string, we are mostly hearing the fundamental tone (actually, the harmonics are also being generated, but the main pitch is the fundamental.
Timbre (color)= # of frequencies played. Tuning fork and flute produce close to a pure tone – we mostly hear the fundamental tone. Violin has a complex timbre – we head
the fundamental and many of the harmonics (overtones) all at the same time.
If I press down on a string, I change the string length, therefore change the pitch (fundamental tone) of the note.
If I lightly press a string, I add in a node – thus eliminating some of the harmonics and making others the main pitch.
Press halfway – get second harmonic – one octave up
Press 1/3 or 2/3 – get third harmonic – 12 notes up (G -> D)
Press ¼ or 3/ 4 – get fourth harmonic – two octaves up (press this at third finger spot, I think)
And so on …
Also show resonance
See link:
Second harmonic
Third harmonic

6. Harmonic Math
What wavelengths can be produced? Only regular divisions of the string … .
Note that the fundamental frequency has half a wavelength (one loop) across the string.
In other words, it has
1 * ½ wave lengths.
As we go up harmonics, we add ½ wavelengths.
Resonance video