Fundamentals of Sound in Physics (and How That Translates to Music)

By Derek Martinez


Though we credit most of our experiences with sound and music to transduction, the actual process of how our brain understands and processes stimuli, we must equally give as much credit to the actual creation of sound in physics.

For this article, the example of how a tuning fork creates sound will be used as it is one of, if not the simplest sounds in nature. If you are not familiar with how a tuning fork is used, this is essentially what it does.


Tuning Fork Physics

Image Credit: "File:Mode Shape of a Tuning Fork at Eigenfrequency 440.09 Hz.gif"by Sudoer41 is licensed under CC BY-SA 4.0

When you strike the tuning fork against a surface, preferably a hard one, and hold it to your ear, you will hear a vibrating, ringing pitch, similar to a bell. Tuning forks are commonly used in medical exams to assess hearing, and also as a method for musicians to tune their instrument or “tune their ears” to a certain temperament. The sound produced from a tuning fork is caused by periodic changes in air pressure at one’s eardrum, and these air pressure changes are caused by the vibrations produced from the tines of the tuning fork. If there are no changes in air pressure around the ear, our brain interprets it as silence. The high and low pressure waves that travel through the air to the ear pushes and pulls on the eardrum at the same rate that the fork produces the waves.



Compressions are the regions in which there is high pressure, and rarefactions are areas where there is low pressure. In the image above, the moments where the tines are closest are rarefactions, and the moments where the tines are furthest are compressions. These regions are then propagated through the air, carrying the sound signal to different locations.


Physical Properties

In this diagram, the upper wave would be a higher pitch and the lower wave would be a lower pitch

The rate of periodic pressure change is called frequency, which we hear as pitch. In a musical context, frequency would translate to our ears as tones/notes. Though western music has 12 individual notes, (including enharmonic equivalents) that obviously does not mean that there are only 12 frequencies that exist. That would be very boring. Frequency is measured in hertz, (Hz) which is cycles, or oscillations per second.



On string instruments, (say a viola because they’re underrated) if you were to place your finger on a string and then play it, and then in the same place wiggle your finger even slightly and play again, you would hear an audible difference, even though you’re technically playing the same note. This is because it has a different frequency, and thus a different Hz value. Hertz are also used in music to tune to a different frequency from normal, such as 432 Hz, which is slightly lower than what is considered the universal tuning system, 440 Hz.


The strength of the pressure fluctuations of waves is called intensity, and our brain interprets it as loudness. In music notation, intensity would essentially be the same as dynamics, which is how soft or loud an instrument is playing at a certain moment. Intensity is measured in decibels, (dB) the threshold of hearing for decibels is 40 dB up to 120 dB, which is known as the threshold of pain. (ouch)


Onset is the time when an actual sound begins, and similarly, duration is how long we can hear the sound, which is measured in seconds. In music, duration and onset is notated as rhythm, but is instead measured as how many beats a note contains.


Envelope is a sound’s characteristic way in how its intensity changes through time. The envelope helps us establish a sound’s quality through 4 measurements. Attack, the portion of the envelope reaches its maximum amplitude, Decay, the reduction of a wave’s amplitude over time, Sustain, the period of time where sound is held before it fades out, and Release, the final reduction of amplitude over time.


Lastly is wave shape, which our ears use to identify characteristics about a sound as well as its relative location. It is how we are able to differentiate between a violin, a trumpet, and an oboe. Throughout our lifetimes, our ears learn to associate certain wave shapes with certain sound sources. In music, the quality of a sound is described as timbre, which is used to describe the different sounds each instrument produces as well as color and tone.

This concludes the basic fundamental physical properties of sound and its relation to music. Whether you’re a musician or not, the next time that you’re listening to your favorite song, be sure to look out for these properties. It can be surprising to see how much physics really contributes to what we hear.



Educational Content:


Q: Why is a tuning fork a prime example of the properties of sound waves?

A: When a tuning fork is struck, it produces an unwavering and ringing frequency that can be used to observe the properties of a sound wave. Since a tuning fork produces a pure sound, it is also less likely that the sound waves will be affected by certain factors. For example, string instruments are very intricate and the sound can change depending on finger placement and right hand position, but a tuning fork just needs to be struck once and produces the same sound every time.


Q: When we listen to music, when frequency is it most likely tuned to? (What is the universal tuning system?)

A: It is most likely tuned to 440 Hz, which in music would translate to an A natural. In the 18th and 17th century, most instruments were tuned to 415 Hz, but gradually over the centuries, the tuning system would continuously rise up to what we hear most today, which is 440 Hz.





Citations

Loy, D. G. (2011). Musimathics: The mathematical foundations of music. Cambridge, Mass: MIT Press.

www.teachmeaudio.com

https://www.physicsclassroom.com/class/sound


Image Credit:

1. "File:Mode Shape of a Tuning Fork at Eigenfrequency 440.09 Hz.gif" by Sudoer41 is licensed under CC BY-SA 4.0

https://ccsearch.creativecommons.org/photos/bf9ea5b1-b8f6-4b90-bd53-adfa084c5a8c

2. "File:OndeVolumeAltoBassoDiversaFrequenza.png" by Mattruffoni is licensed under CC BY-SA 4.0 International License https://commons.wikimedia.org/wiki/File:OndeVolumeAltoBassoDiversaFrequenza.png

https://creativecommons.org/licenses/by-sa/4.0/deed.en

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