Have You Ever Wondered How Guitars Make Noise?

Whether it is your favourite musician strumming a tune, or your significant other serenading you, you have probably heard of the ubiquitous guitar. Both cool-looking and portable, it is the to-go instrument for impressing others with your complete mastery of Twinkle-Twinkle-Little-Star. But have you ever thought of how your guitar works? The scientific aspect of music? Well if you haven't, this is the time to pick up some new information and use it to impress your brainier friends. You can even write a song about it and perform it on your guitar!

Sound

All sound starts with something that vibrates, therefore vibrating the air molecules and thus our eardrums. Sound propogates through air, water and most compressible forms of media as longitudinal waves. The source, in this case a guitar string, vibrates to a particular frequency, creating vibrations in the surrounding medium. As these vibrations continue, they form waves that propogate through the medium at the speed of sound (about 343m/s). Most vibrations produced by musical instruments and the human voice are approximated by a particular kind of vibration, called simple harmonic motion.

Tuning fork in water


Simple Harmonic Motion (SHM)

In Physics, simple harmonic motion is a type of periodic motion, where the restoring force is obeys Hooke's law, which just means that the force directly proportional to the displacement. If we double the displacement from equilibrium, the force acting to return the object to the equilibrium position also doubles. Most springs obey Hooke's law. The more you stretch the spring, the larger the force.The simplest of all vibrations occurs when there is a Hooke's law force and no friction acts. This type of motion is commonly used for vibrations in musical instruments. An example of SHM would be a pendulum bob, with a relatively small angle and amplitude (like in a grandfather's clock). Another example would be the way guitar strings vibrate.

Period (T) and Frequency (f)

A periodic motion, as its name suggests, has a period, T, which is measured in seconds. The period is the time is takes for the vibrating object to make one oscillation and return to its original position. This number is closely related to frequency, f, which is the number of periods that are measured in one second. This means that frequency is the inverse of period (1/T). Frequency is measured in Hertz.

Guitar strings

When a guitar string is at rest, it is at its equilibrium position. When the strings are strummed, they vibrate, oscillating from side to side. The displacement, the distance of the string from its equilibrium position, changes constantly. The maximum displacement, also called the amplitude, is when the string reaches a certain distance and moves in the opposite direction.

Not only does the displacement change over time, the velocity (speed) of the object(can be a point on the string) is also constantly changing. As the object reaches its maximum displacement, it slows down, reaches a point where its velocity is zero, and turns around. The force acting on the strings that cause it to change velocity is called the restoring force, which acts to push the object back towards its equilibrium position. This restoring force is the potential energy stored in the stretched guitar string, much like how a stretched rubber band stores energy.

Sound Propagation

As a guitar string vibrates, it transfers its momentum to the air molecules around it, setting them into motion. The frequency at which these molecules vibrate is equal to the frequency of vibration of the guitar string.

The back and forth vibrations of the surrounding air molecules creates a pressure wave which travels outward from its source (i.e. the guitar). This pressure wave consists of compressions and rarefactions, regions of high pressure and low pressure respectively. This alternating pattern of compressions and rarefactions is known as a sound wave, and that is what our ears pick up.

It is notable that guitar strings are not audible on their own. This is because the string itself disturbs very little air since its small surface area makes very little contact with surrounding air molecules. However, if the guitar string is attached to a larger object, such as a sound box or the body of the guitar, more air is disturbed when the sound box vibrates at the same frequency as the strings. Because of the larger surface area, the sound produced is now audible.


Slow Motion Guitar Strings

Cool, huh? Note how the guitar strings vibrate left and right with the equilibrium position being its position at rest.










References:
http://homepages.ius.edu/kforinas/S/Periodic.html
http://www.sparknotes.com/physics/oscillations/oscillationsandsimpleharmonicmotion/section2.rhtml
http://www.physicsclassroom.com/class/sound/u11l5b.cfm
http://www.bsharp.org/physics/guitar
http://www.physicsclassroom.com/class/sound/u11l5b.cfm