### Resonance

Objects have frequencies that they prefer to vibrate at. If you try to vibrate it at a different frequency, the vibrations will be dampened and eventually die out. If you try to vibrate it at its preferred frequency, the vibrations will be reinforced and the object will resonate.

Some examples of resonance:

• a standing wave on a skipping rope
• the note you get when you blow into a half-full beer bottle
• the vibration in the sounding board of a violin
• a swing swinging higher when you push it just right (or when you "pump" just right while sitting on it)

If you try to make an object vibrate at twice its favourite resonating frequency, it will not respond very well. If you try to make it vibrate at three times its favourite resonating frequency, it will again resonate -- though not as much as at the lower resonating frequency. This pattern repeats -- every odd multiple of the lowest frequency will be an effective resonanting frequency:

 multiple of favourite frequency resonance? 1 x yes 2 x no 3 x yes 4 x no 5 x yes

For a half-open tube that is 17 cm long (a typical length for an adult male's vocal tract), the preferred frequencies are 500 Hz, 1500 Hz, 2500 Hz, 3500 Hz, and so on.

We often diagram the frequency response curve of a tube. This shows for each frequency how much a tube would resonate if you gave it vibrations at that frequency. The frequency response curve for a 17 cm long vocal tract held in neutral position (i.e., the position for schwa) looks like: