Forced Vibrations

• A system with a driving force will force a vibration at its frequency

• When the frequency of the driving force equals the natural frequency of the system, the system is said to be in resonance

Standing Waves

• When an incident wave interferes with a reflected wave to form areas of constructive and destructive interference.

Nodes are where the resulting wave remains stationary.Anti-nodes are where the resulting wave has max amplitude.

Other Examples of Resonance

• Child being pushed on a swing• Shattering glasses• Tacoma Narrows Bridge collapse due to

oscillations by the wind• Upper deck of the Nimitz Freeway collapse

due to the Loma Prieta earthquake

1989 Loma Prieta earthquakeAka Quake of '89

World Series Earthquake

Resonance

Resonance: a vibration of large amplitude in a mechanical or electrical system caused by a relatively small periodic stimulus of the same or nearly the same period as the natural vibration period of the system.

http://www.merriam-webster.com/dictionary/resonance

How many wavelengths?

1

2

1 ½

½

How does a Guitar String Vibrate?

½ = L

= 2L

L

What is the velocity of the wave on the string?

v = f = 2L

Different Frequencies

• How can I change the frequency (note)?

Harmonics!

• When you sound the guitar note, you hear other frequencies.

How does a Guitar String Vibrate?

How does a Guitar String Vibrate?

How does a Guitar String Vibrate?

Fundamental frequency

2nd Harmonic

3rd Harmonic

4th Harmonic

= 2L

f2 = v/L

f3 = 3v/2L

f4 = 2v/L

f1 = v/2L

= L

= 2/3 L

= ½ L

Summary

f = nv/2L

n is the # of antinodes or harmonic

• Fundamental Frequency is the LOWEST frequency

• All harmonics are multiples of the fundamental frequency (e.g. f1 = 50 hz, then f2 = 100 hz, f3 = 150 hz, etc)

= 2L/n

Fundamental frequency1st Harmonic

2nd Harmonic

3rd Harmonic

4th Harmonic

How does a Guitar String Vibrate?