# Chapter One: An Acoustics Primer

#### 4. What are the characteristics of sound waves? | Page 2

What is Simple Harmonic Motion (SHM)?

Simple harmonic motion (SHM) is a type of periodic motion characterized by a restorative force equal and opposite the source of displacement...fortunately for us, our surrounding atmosphere provides that force for sound waves, returning it to the ambient pressure when the source of displacement is at rest. Demonstrations of simple harmonic motion are approximated by the movement of a small-angle pendulum and/or a mass/spring example, both of which are shown on the videos below. The periodic movements of both are represented as tracing a sine wave in the time domain, which takes the shape of its mathematical namesake, the sine function. A sinusoidal wave (which also includes a cosine wave) is the only waveform that produces a single frequency, as can be seen in the waveform chapter. With any minute deviations in the sine shape, additional frequencies will be generated.

click video image to play/pause

### Low-angle Pendulum SHM

click video image to play/pause

### Mass/Spring SHM

Simple harmonic motion has a single resonant frequency

In the case of the pendulum example above, the resonant frequency can be calculated as . In the case of the mass/spring example above, it can be calculated as .

Later in this text, it will be shown that cavity resonators like a pop bottle, work very much like the mass/spring example to produce a single resonant frequency. In fact, the term acoustic mass is often applied to these resonators.