• Standing waves in a tube open at both ends are constrained to have specific wavelengths and frequencies
• Standing waves in a tube open at only ONE end are constrained to have slightly different specific wavelengths and frequencies
• Resonance occurs when some periodic force drives a system with a frequency close to the natural frequency of the system
• If two waves with ALMOST, but not quite, the same frequency interfere, the result is a wave with a time-varying amplitude; we call the slow variations in amplitude "beats"
• The beat frequency is simply the difference between the frequencies of the two original waves
• Complex waves are combinations of a fundamental frequency and some of its higher harmonics
• The different shapes of complex waves produced by different musical instruments are detected by our ears as different timbres
• Any complex wave can be expressed as the sum of simple sine and cosine waves; this is called Fourier analysis

Recall that we considered earlier the case of standing waves on a string:

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  Today, let's focus on a different type of standing wave: the pressure wave in a column of air.

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Copyright © Michael Richmond. This work is licensed under a Creative Commons License.