Digital Sound & Music: Concepts, Applications, & Science, Chapter 2, last updated 6/25/2013

8

quarter cycle, it has a 90

o

offset, and so forth. In Figure 2.5, the red wave has a 90

o

offset from

the blue. Equivalently, you could say it has a 270

o

offset, depending on whether you assume it

is offset in the positive or negative x direction.

Figure 2.5 Two sine waves with the same frequency and amplitude but different phases

Wavelength, , is the distance that a single frequency wave propagates in space as it

completes one cycle. Another way to say this is that wavelength is the distance between a place

where the air pressure is at its maximum and a neighboring place where it is at its maximum.

Distance is not represented on the graph of a sound wave, so we cannot directly observe the

wavelength on such a graph. Instead, we have to consider the relationship between the speed of

sound and a particular sound wave‟s period. Assume that the speed of sound is 1130 ft/s. If a

440 Hz wave takes 2.27 milliseconds to complete a cycle, then the position of maximum air

pressure travels in one wavelength, which is 2.57 ft. This

relationship is given more generally in the equation below.

Let the frequency of a sine wave representing a sound be , the period be , the

wavelength be , and the speed of sound be . Then

or equivalently

f c /

Equation 2.3

Figure 2.6 Wavelength

2.1.3 Longitudinal and Transverse Waves

Sound waves are longitudinal waves. In a longitudinal wave, the displacement of the medium is

parallel to the direction in which the wave propagates. For sound waves in air, air molecules are

oscillating back and forth and propagating their energy in the same direction as their motion.

You can picture a more concrete example if you remember the slinky toy of your childhood. If

you and a friend lay a slinky along the floor and pull and push it back and forth, you create a