Music to Your Ears

Have you ever wondered what causes your favorite instrument to create sound? The answer is rooted in the physics of waves. There are many different types of waves: transverse, longitudinal, and standing. Transverse waves move perpendicular to the direction of the wave, longitudinal waves move parallel to the direction of the wave, and standing waves appear stationary in space. 

Basic elements that define a wave are its wavelength, period/frequency, and speed. A wavelength (w) is the distance over which a wave repeats itself. The period (T) is the time required for a single wavelength to pass a defined point. The frequency (f) is inversely related to the period. Finally, speed (v) is the same as if we were referring to the speed of a car: the amount of distance covered over time.

​Instruments produce sounds via standing waves. Standing waves are composed of nodes (the point at which the wave appears to have zero displacement) and antinodes (the point at which the wave appears to have maximum displacement). The frequency - otherwise known as a harmonic for standing waves - is determined by the fundamental (first) harmonic. Consider part of the derivation shown below.

So what does any this have to do with instruments? Consider a guitar. It is composed of strings of varying weight, length, and tension. In a string, the wave speed (v) is dependent on the mass per length (m) and tension (F), as shown in the equation at right. ​

Substituting the equation for the speed of a wave in a string into the equation for the frequency of a standing wave, you find that the frequency of a standing wave depends on the weight, length, and tension of the string, as shown at right. Higher frequencies cause higher pitches. Likewise, lower frequencies cause lower pitches. Therefore, the frequency of the string plucked changes when you adjust string tension when tuning a guitar, or changing the length of the string by moving your finger along the neck.

So, at your next jam session you can impress your friends with both your musical skills and Physics knowledge.