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
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.
Jan 03, 2016
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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?
Related Documents
