Waves and Sound


Sound is made of waves in a medium like air or water.   The structure of these waves is difficult to understand in terms of familiar acoustic concepts, like pitch, timbre, rhythm, and cadence.  With certain analytical tools, however, we can make images of sound which can help us to see these and other qualities in sound.


These are half-second clips of three very different sounds:


Audio waves

These are graphs of changes in air pressure (or water pressure, for the whale song), usually sampled thousands of times each second.  The changes are variations from the average air (or water) pressure.  If the pressure is unchanging, there is silence.

The easiest feature to see is the energy carried by the wave.  Energy corresponds to the volume knob on a radio: the more energy in a signal, the louder it is.  

The amount of ink used to draw the wave is an indicator of how much energy is in the signal at a given moment.   We might see this more easily by showing just the energy at each moment:


Same waves as above, energy

Other than volume it is difficult to recognize these pictures.  We might wonder if the sounds are high or low pitched, whether there is music or harmony, or whether it is simply noise.  Discovering structure in waveforms is the topic of this discourse.

•Digital waveforms are made up of individual samples

If we zoom in on the waves, we can see the actual fine structure of the wave, representing measurements of air pressure:


Successive zooms of the Cello example, from above

If we continue to zoom in on the waves, we can see the actual digital samples:


Successive zooms of the Cello example, from above, down to the sample level

It is a characteristic of digital sound, such as audio CDs, that the waves are represented by measurements of air pressure at specific moments in time.

•Waves can be added to combine sounds

To find out what two different sound waves would sound like together, for example to convert a stereo recording to mono, we can simply add the waves.


Left: a tone increasing in volume.  Right: a steady tone

Thus, the two waves above can be added to produce the one below:


The sum of the two waves

This can lead to the apparent paradox that for any sound, there is another sound that, if played simultaneously, will cancel the first.  This is difficult to arrange, or the world could be a quieter place.


Adding these two opposing waves results in silence.

© 2003 N. Resnikoff

Converted by Mathematica  (February 12, 2003)