Resonance

Every oscillating system has a natural frequency :

• Pendulum / mass-spring : time : period T = 1/f
• Pipes / stretched string : frequency of standing waves

Most systems are damped by friction :

e.g. pendulum comes to a halt

What if we drive (or pulse ) the system at its natural frequency ? (i.e. add energy):

one gets

HUGE

Even glass has a resonant frequency.

If Engineers do not take into account resonances:
The destruction of Tacoma Narrows bridge .
This is actually an example of a sustained oscillation .

Can you break a glass with your voice?

Review

What are examples of damaging resonance?

• Takoma Narrows Bridge(wind)
• buildings in earthquake(vibration)
• wineglass next to speaker(sound)

Can we use resonance to our advantage?

• resonant cavities : guitar, violin, drum
• stereo speakers
• acoustics
• lasers(optical resonance)

Resonance

• 1-Dimension = line - string
• 2-Dimensions = flat plane - drum head
• 3-Dimensions = volume - box