It is too loud!

In the authors'¹ own words, “Loudness is a psychological term used to describe the magnitude of an auditory sensation.” “If loudness depended only upon the intensity of the sound wave producing the loudness, then measurements of the physical intensity would definitely determine the loudness as sensed by a typical individual and therefore could be used as a precise means of defining it. However, no such simple relation exists.” The article describes methods and calculations, defining relationships between a sound's perceived loudness and some of a sound-wave's physical properties. As a result, “This work has resulted in better experimental methods for determining the loudness level of any sustained complex sound and a formula which gives calculated results in agreement with the great variety of loudness data which are now available.”

The article was originally written to improve an understanding of hearing and, in so doing, to improve the telephone system. However, controlling loudness is ubiquitous. One often wants to control the loudness of a radio, a cell phone, the television, or an unhappy baby. We do not want “noise” from the street, the airport, the bar down the street, or our neighbors to be too loud. If you want to make the music you are listening to twice as loud, how much should you change its physical intensity? Controlling loudness is not unique to a particular sound. Any sound can be “soft” or “loud.” Changing almost any acoustic variable may affect loudness. Change the frequency content of a sound and its perceived pitch might change but so might its perceived loudness. Fletcher and Munson¹ were among the first to develop psychophysical relationships between loudness perceptions and several physical properties of sound. Those relationships facilitated an ability to double the loudness of music; regulate the loudness of airplanes, cars, trains, or restaurants; control the loudness of the sound of a hearing aid so it is not uncomfortable; and improve an understanding of the psychophysical relationships between auditory perceptions and acoustic variables.

The most cited part of their article¹ concerns “equal-loudness contours” as shown in the graph. Equal-loudness contours display the level (dB above a reference intensity at the approximate threshold of hearing) of a 1000-Hz reference tone required for a subject to subjectively match the perceived loudness of a test tone as a function of test-tone frequency. Each contour represents different test-tone intensities (dB above the reference intensity). A 1000-Hz tone is about in the middle of the frequency range of human sound perception and has a low detection threshold. Each equal-loudness contour indicates that tones with the frequencies and intensities indicated by a contour are all judged equally loud. And, to be equally loud, tonal sounds of different frequencies have to be of different intensities. So, unlike physical frequency and intensity, which are independent acoustic variables, frequency and loudness are not independent. The implications are many. Musical sounds which vary in frequency may also vary in loudness, something a composer or conductor appreciates. Low-frequency or high-frequency sounds are not perceived to have the same loudness as mid-frequency sounds—this has significant consequences for how a sound's physical intensity may affect annoyance and/or hearing loss. Importantly, loudness grows with sound intensity at different rates, depending on frequency, which is of significant importance in fitting hearing aids. The equal-loudness contours were the basis for additional experimentation by Fletcher and Munson,¹ regarding the loudness of complex sounds consisting of a mixture of different frequencies.

In the early 1940s, the American Standards Institute developed a standard for sound-level meters, which was revised over time.² Fletcher and Munson's equal-loudness contours¹ (see the graph in Fig. 1) and calculations helped define a sound-level meter's measure of intensity. One of these measures, decibels using the A weighted scale (dBA), became the standard sound-level measure used by all sound-level meters. A wide variety of processes, standards, policies, regulations, and laws are based on dBA. Fletcher and Munson's equal-loudness contours were remeasured and recalculated for revised loudness standards.^3,4 Additionally, methods were developed and standardized to calculate loudness for a variety of different acoustic waveforms.^5,6 Every loudness knob on a device, every policy used to regulate or measure sound intensity, and every hearing-aid fitting are directly related to Fletcher and Munson's experiments and calculations.

W.A.Y. is supported by the National Institute on Deafness and Other Communication Disorders and Facebook Reality Laboratories, and he is grateful for the assistance of Dr. M. Torben Pastore, Dr. Yi Zhou, and Ms. Kathryn Pulling.