Waves and Sound

Last week, we studied waves, sound, and music as it relates to math and physics. Two types of waves we studied are transverse and logitudinal. They differ in that the movement of the medium in a transverse wave is perpendicular to the direction of energy transport. However, the movement of the medium in a longitudinal wave is parallel to the velocity of the wave. These are both forms of mechanical waves, which require a medium to travel, as opposed to electromagnetic waves, which can travel in space due to electric and magnetic fields. Sound waves are also mechanical waves. Standing waves, or "stationary waves," occur when a wave remains in a constant position, at certain frequencies called harmonics. Music is made up of a blend of harmonics.

Standing waves occur in stringed instruments, like the guitar displayed above, that are tied down at both ends. The first harmonic of a stringed instrument is the lowest frequency at which at standing wave will occur. The second harmonic is the two times the fundamental frequency, the third harmonic is three times the fundamental frequency, and so on. The first harmonic is one half of the wavelength, as opposed to woodwind instruments where the first harmonic is one fourth of the wavelength. Woodwind instruments are those where the pipes are closed at one end. These instruments only have harmonics of odd numbers such as the first harmonic, third harmonic, fifth harmonic, and so on. For both types of instruments, air molecules come together at the nodes, where there is no air movement. In between the nodes, however, there is high air movement. Sound, in fact, is the movement of air molecules that move our ear drums. Thanks to harmonics and physics, this sound appears as music!