What is Sound?

Vibrations and Sound

Sound is the vibrations of molecules in a medium, usually air. When you speak or play an instrument, you cause the air molecules to vibrate. For example, when you pluck a string on a guitar, it begins to vibrate rapidly. These vibrations cause the surrounding air molecules to compress and expand in a repeating pattern. The string displaces nearby air particles, which in turn push on their neighboring particles. This creates a series of pressure waves known as sound waves that radiate outward from the vibrating string. The pockets of high air pressure undergo compression and the pockets of low are undergo rarefaction.

As the sound waves move through the air, they eventually reach your ears. The waves cause the air near your ear canal to vibrate, and this vibration travels through the canal until it hits the eardrum. The eardrum is a thin membrane that responds to these changes in air pressure. When the sound waves strike the eardrum, they cause it to vibrate at the same frequency as the sound wave. A sequence of transformations then occur through various mechanisms, ultimately translating the sound into electrical signals that are sent to the brain. This process of converting sounds into electrical signals is known as transduction.

Modeling Sound with Waves

This vibration causes periodic changes in air pressure that can be modeled using sine waves. A microphone captures these changes and converts them into an electrical signal.

Here are some basic properties of sound:

• Amplitude describes the intensity of the vibrations, which determines the volume or "loudness" of the sound.

• Frequency describes how fast the vibrations are, which affects how "high" or "low" the sound is. This is also called the pitch of the sound. The wavelength of the sound wave is inversely related to the frequency. (The product of frequency and wavelength is a constant, so if you double the frequency of a wave, you cut the wavelength in half.) The period of a wave is the time taken to complete one cycle. Period is the reciprocal of the frequency, so period times frequency is equal to one.

• Phase describes where a sound wave is in its periodic cycle. From the listener's point of view, there is no way to tell the phase of a sound wave. However, it becomes important when processing the audio in a computer.

A wave can be represented using the following formula.

$$x = A \sin(B(t - C))$$

In this formula,

• $A$ determines the amplitude,
• $B$ determine the frequency,
• $C$ determine the phase,
• $t$ is time,
• $x$ is the position of a pocket of air pressure as a function of time.

Timbre

If a piano and a guitar both play the same note at the same volume, why do they sound different? According to the simlpe $x = A \sin(B(t - C))$ model of a sound wave, if both waves have the same amplitude, frequency, and phase, then the sounds should be identical. However, this model is not a complete description of how sound works in the real world.

Real sounds are more accurately described as a sum of multiple waves of different frequencies and amplitudes. When two waves are added together, they form a new periodic function that has a unique sound.

The unique combination of various individual sine waves that make up a sound for an instrument is called the instrument's timbre (pronounced "tamber").