The Understanding of Sound Energy

Diego Celis
October 21, 2018

Submitted as coursework for PH240, Stanford University, Fall 2017


Fig. 1: The stereocilia in a frog's inner ear. (Source: Wikimedia Commons)

The existence of sound is beautiful. It allows us to enjoy music, to communicate with each other, and to better understand our surroundings. However, we seldom stop to think about how our hearing is possible and what causes it. And the truth is that, like most things, we can ascribe this wonder to the movement and translation of energy.

Sound as Energy

Sound travels through fluids by introducing small, and sometimes large, perturbations in pressure. The patterns by which these perturbations travel are known as sound waves. We can measure a sound's magnitude via its acoustic pressure level (APL), which is measured in decibels (dB), although the quantity is truly dimensionless. According to the International Electrotechnical Commission, the agreed-upon standard for calculating decibels is

APL (dB) = 20 log10 (p/p0)

where p is the root mean square sound pressure (Pa) of the source of interest and p0 is the reference sound pressure (Pa). [1] An important thing to note is that the decibel system is a referential system, which means that it operates and takes meaning as a magnitude relative to another. This is unlike absolute measurements, such as temperature or length, which have concrete and theoretical minimums (e.g. 0°K or 0 m). This very nature of measurement posits a very important question: what should the reference sound pressure be?

An often used reference is 20 μPa, which is generally regarded to be the threshold of human hearing (i.e. the lowest sound an average, undamaged human ear can perceive). [2] This establishes a standard from which people can compare different levels of loudness, or energy, that a particular sound source emits. Because decibels are referential, the amount of energy emitted is also referential. In other words, decibels can be used to calculate the amount of energy (J) of a source object's emission relative to (as a factor of) the reference object's emission.

Interpreting Energy

Our bodies generally come equipped with sophisticated mechanisms to interpret the information encoded in a sound wave. When a sound wave moves about its medium, it displaces the fluid it lives in in an oscillatory manner via compression and expansion due to pressure changes. Because of this, sound waves are considered mechanical waves, and it is through these environmental operatives that our ear decodes sound waves into various things, like the music we listen to, the voices we hear, or the noise in the subway.

In particular, our ear understands sound via its hair cells. Around 16,000 hair cells live in an ear's basilar membrane, with each hair cell containing around 100 stereocilia. [3] It is through these over a million receptive organelles that our ear understands the various minute, and sometimes not so minute, changes in pressure due to sound. An example of such organelles is shown in Fig. 1.


From a systems perspective, sound can be interpreted as a message that is encoded by an emitter, transmitted through a medium, and decoded by a receptor. Emitters can come in all different shapes, sizes, and backgrounds, from a masterful orchestra playing a piece to an angry driver honking on the road. Mediums can affect the message, such as water dampening the sound waves' intensities or like a vacuum (the absence of a medium!) completely preventing the transfer of the message in the first place. Thankfully, in the most general case we have the right receptor - two, in fact - to perceive, appreciate, and tolerate (mostly) all sounds.

© Diego Celis. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.


[1] "Letter Symbols to be Used in Electrical Technology Part 3: Logarithmic and Related Quantities, and Their Units," International Electrotechnical Commission, IEC 60027-3, Ed. 3.0, 19 July 2002.

[2] R. J. Roesser and M. Valente, Audiology (Thieme, 2007), p. 240.

[3] A. Hudspeth,"The Cellular Basis of Hearing: the Biophysics of Hair Cells," Science 230, 745 (1985).