Pitch Definition (Physics): Understanding Frequency Of Sound

You've probably heard of music virtuosos with "perfect pitch," but what is pitch? And what of the opera singer who can sing a note so pure it breaks a crystal glass? All of these phenomena are related to sound wave frequency.

Sound waves are vibrations in a medium, which can be perceived by the human ear. Oscillations in a medium such as air propagate from the source to you transferring the vibration to your ear drums, which your brain interprets as sound.

A wave is described by its ​wavelength​ (the distance between wave peaks), its speed (how fast it propagates through a medium) and its ​frequency​.

The frequency of a sound wave is how many times it vibrates per second, measured in Hertz, where 1 Hertz (Hz) = one cycle per second (1/s). The wavelength of a sound wave is the distance between two consecutive wave peaks. It is typically measured in units of meters (m). The speed of a sound wave, ​v​, is directly related to frequency ​f​ wavelength ​λ​ via

\(v=\lambda f\)

In a musical instrument or in your voice box, standing waves create specific sounds or musical notes that correspond to the frequency of vibration.

In psychoacoustics, the ​pitch​ of a sound is essentially a description of the frequency of the sound. Different pitches correspond to different frequencies. High pitch means high frequency, and low pitch means low frequency.

Pitch can also be described as the quality of a sound that allows you to label it as "higher" or "lower" to your ear. Someone with perfect pitch has an ear so attuned that they can identify a note exactly by hearing it. Especially talented individuals can even play an entire piece of music after hearing it once.

Just how does an opera singer break a glass with her voice? By singing a pure note which matches the natural frequency of vibration of the glass. This causes the glass to vibrate with increasing amplitude until it shatters!

You may have heard singers being critiqued and told they sound "pitchy." What this means is that they aren't hitting the notes quite right and some are falling flat (slightly too low in pitch) and others sharp (slightly too high in pitch.) In essence, "pitchy" is the less extreme version of being "off key" which means not really hitting any of the notes at all.

There are many aspects of sound one might wish to describe. One of the most obvious is the ​loudness​. A common way of presenting perceived loudness of sound is by using the decibel (dB) scale, where sound intensity is in decibels is:

\(\text{intensity in decibels}=10\log{\frac{I}{I_0}}\)

where ​I​ is the sound power per unit area in watts per square meter, and ​_I₀_​ = 10^-12 W/m² is considered the threshold for human hearing.

The decibel scale is useful because humans don't perceive loudness linearly. That is, a sound with twice the intensity can seem like more than twice as loud when it started out quiet, and less than twice as loud if it started out somewhat loud already. The decibel scale provides numbers more consistent with our perceptions.

​Timbre​ is the perceived sound quality of a note in music. While you might play the same note on a guitar as on a piano, your ear can tell the difference. When the guitar string is plucked, producing a given note by vibrating at its fundamental frequency, it is simultaneously vibrating at the overtone values as well but with much smaller amplitude (lower volume).

The same happens when the piano key is played, and the differences in physical properties of these instruments lends to different combinations and relative strengths of overtones, allowing you to distinguish between the two instruments.