The Physics Underlying Harmony

Transverse & Longitudinal Waves Since sound is just air waves, let's start by looking at the underlying physics behind waves. The waves most people are familiar with are waves in a body of water, like ripples in a pond, or waves on the ocean. As the waves travel through the water, the surface of the water moves up and down in a series of peaks and troughs, like shaking out a bed-sheet. Notice how the wave’s movement is perpendicular to its vibration - the water ripple travels across the water horizontally but it vibrates the water up and down, vertically. A wave that act likes this is known as a Transverse wave (SLH-PAP). Sound, on the other hand is a Longitudinal wave, which is where the vibration happens parallel to the direction of motion (SLH-PAP). Imagine stretching out a slinky, and instead of shaking it up and down to make a wave (a transverse wave) you pulsed it back and forth slightly; this is a Longitudinal wave.

Fig 1: Ripples are an example of Transverse waves (Beauregard)

Similarly, when an object vibrates it pushes the air molecules around it out, which bump into other air molecules and transfer their inertia into them which causes them to move out, and so on, leading to an alternating series of regions where the particles are more compressed (bunched together) and have a higher pressure with regions where the air molecules are more rarefracted (spaced out), leading to an area of lower pressure.

Fig 2: Example of a Transverse Wave (Wikimedia Commons)	Fig 3: Example of a Longitudinal Wave (Wikimedia Commons)

Graphing Sound Waves

Fig 4: Mapping a Sound wave onto a Graph (Cai, He, Zhu, Wang)

Despite looking different, both types of waves have the same basic mathematical properties, and we can take a longitudinal wave and "turn it into" a transverse wave by graphing it.  We let the x-axis represent the distance traveled, and the y-axis represent the pressure of the air at that particular distance, as seen in Figure 4 to the left.  The bottom graph is much easier on the eyes than the top one, but both represent the same wave. Keep in mind that sound is three dimensional; it propagates out from a central point in all directions until it runs into a barrier.  When we use graphs, we are only looking at a slice how the wave is filling the space around us.