Introduction to Acoustics

When you listen to amplified sound, you

hear two things – the sound of the speakers and the sound of the room.

When you listen to amplified sound, you hear two things – the sound of the speakers and the sound of the room. Notice that I said the sound “of” the speakers, not the sound “from” the speakers. This is because the direct sound coming from the speakers is “colored” by the speakers themselves. This coloration is caused by the frequency and phase response properties of the speaker, the directional characteristics of its drivers, and reflection effects of its enclosure. Obviously, the speaker itself is a major contributor to the sound that is heard in the room.

Every speaker imparts some combination of these factors to the sound emanating from it. No two speakers sound exactly alike, and none provides perfect reproduction of the electronic signal being fed into it. However, thanks to the ingenuity of engineers, mathematicians, and designers over the years, audio speakers do an amazing job of reproducing sound in a fairly accurate fashion. Some obviously do this better than others,

The properties of speakers are treated in a separate page.

The sound of the room has a major effect on the sound perceived by the listener.

The other thing you hear besides the sound of the speakers is the sound of the room in which the sound is being reproduced. The sound coming from the speakers is partially absorbed and reflected by the various walls, surfaces, and objects in the room in frequency-sensitive ways that alter the sound being perceived by listeners, The degree to which a particular frequency is absorbed and reflected by an object or surface is measured by several properties. Absorptivity (α) is a measure of how much of the sound is absorbed by the body or surface. Reflectivity (ρ) is a measure of how much is reflected, and Transmissivity (τ) is a measure of how much passes through the object or surface. The sound you hear in a room is that which is heard directly or reflected. The frequencies you do not hear are those that are absorbed by or transmitted from the room. Thus, both the sound level and its frequency curve are modified by the room.

Another phenomenon that is occasionally discussed is called diffusion. A diffusion device doesn't directly reflect or absorb sound but scatters it in many directions. This is a difficult property to measure, but various devices with irregular surfaces are manufactured to take advantage of this property. Depending on the material from which a diffuser is constructed, it will have a certain degree of reflectivity and absorptivity that will be frequency dependent to some degree.

Details of Sound Perception

To be precise, there are at least five things that determine the perception of sound in a room.

When you get down to the details, there are at least five things that determine one's perception of sound in a room:

  • The sound of the speakers
  • The sound of the room
  • Human hearing characteristics
  • Individual hearing capability
  • Individual perception training and experience

We have covered the first two items in the sections above. Now let's discuss the other three briefly.

Human Hearing Characteristics

A trained audio technician is aware of what is called the Fletcher-Munson effect, or equal-loudness contours. This has been covered in another page. We hear high frequencies better than low frequencies. Our hearing is most acute in the range of 800 to 6000 Hz and even more acute between 2 and 4 kHz. A sound at 80 Hz must be 30 dB louder to be perceived at the same level as one at 1000 Hz. Thus, our ability to hear sound is a function of its level as well as its frequency.

Individual Hearing Capability

Our ears are amazing organs. A fully functioning human ear can hear sounds that range in frequency from about 30 Hz to 16 kHz and a range of around 140 dB, but any sound above about 85 dB is considered damaging to the ear*. I used a somewhat narrower frequency range than the normally quoted range of 20 Hz to 20 kHz because frequencies below about 30 Hz are felt more than heard, and it is a very rare female who can hear frequencies above about 16 kHz. The hearing of most males tops out around 12 kHz. Depending upon our sound exposure history, most of us have some degree of hearing loss as we age, particularly at the higher frequencies. It only takes one very loud sound, such as an explosion or gunshot to damage our hearing capability forever. Most males have some degree of high-frequency hearing loss, for various reasons, Those whose hearing loss is substantial often resort to hearing aids, These compensate for hearing loss above about 500 Hz and definitely impart a change to the sound that we hear. Because of these kind of factors, the sounds that we hear depend on our individual hearing capability.

Here's an overview by Marina Vasquez of how our ears work in order to receive sound and send it to the brain for coding. Also see Human Perception of Sound.

Individual Perception Training and Experience

"Hearing is much more than receiving sound. It also involves the brain's ability to process sound waves into usable information. " Christopher Muscato

Chris describes four stages of auditory processing - awareness, discrimination, identification, and comprehension. Our perception of sound depends on the degree to which we have developed each of these stages and is a function of our experience as well as our training, Trained sound technicians have the ability to perceive and interpret sound better that an average listener, and it is important to continue to develop this capability, Moreover, a good technician knows what to do to achieve the best possible sound in a room based on what he or she hears and also recognizes the limitations involved, which are based on all of the factors discussed on this page.

Casey Connor has published a 5-part series on Psychoacoustics that gives some interesting examples of human perception of sound. I recommend that you view all 5 of these, as each one demonstrates important sound phenomena.


*_This ability of the ear to hear such a large range of intensities is called adaptation. If you want more information about this, you might like to read about some research that casts some doubt on previous views of this process.

Wave Propagation

The diagram to the right shows how sound waves from a speaker consist of compression and rarefaction of air molecules that result in sound that can be perceived by a listener. These are called longitudinal waves because the air displacement is in the same direction or opposed to the direction of travel of the wave. The interesting thing is that the air molecules don't travel far; they just oscillate or move back and forth. Only the wave itself propagates. Such sound waves can be described mathematically and conceptually as a sine wave or a combination of sine waves, as shown. Sound from a source tends to propagate in all directions, but most sound emitters have some degree of directionality that is frequency dependent. Primarily because of this spread or dispersion, the sound level decreases as distance from the source increases. As the waves encounter walls or other objects they are reflected or scattered into wave fronts that interact with the original waves and either increase or decrease the pressure level of the waves.

Sound waves are characterized by their frequency or wavelength, their amplitude (pressure or intensity), and their speed. Frequency is inversely proportional to the wavelength. The two are related by the equation w= s/f, where f is frequency in Hz, w is wavelength, and s is the speed or velocity of the wave. For sound waves, the velocity is 343 meters/sec or about 1130 feet/sec. Thus, the wavelength of a 100 Hz sound wave is 1130/100 = 11.3 feet. (The speed of sound is a function of the density of the medium and the temperature. The value of 1130 ft/s is for air at 20 degrees C. )

Sound can also be described or analyzed in several ways. Examples of the terms used are pitch, duration, loudness, timbre, and sonic texture. Pitch is related basically to frequency. It is a psychological precept that does not map simply onto physical properties of sound. The American National Standards Institute (ANSI) defines pitch as the auditory attribute of sound according to which sounds can be ordered on a scale from low to high Go here for details.

Timbre has to do with the subharmonic makeup of a sound, described as the time-varying pattern of spectral components by which a sound may be recognized. Thus, a violin can usually be distinguished from a guitar due to the timbre of the sound produced by each instrument. Sonic texture is a term that incorporates several characteristics, such as pitch, timbre, attack and decay of the sound envelope. Duration describes the length of time of the sound envelope. For example, a clap or a drum strike may have a very short duration, while a plucked string may have a longer duration. Loudness has to do with the sound pressure generated by the sound, The loudness of a drum depends on how hard it is struck, for example.

Room Effects

"The character of the room is easily responsible for 40 to 50 percent of the sound of the speaker...."

( Will Eggelston, Genelec, Pro Sound News, Feb.2021).

As discussed previously, the sound of a room is a function of the properties of its containment surfaces and any objects that are in the room. The surface and objects cause reflection and scattering of the sound waves and results in interference that reduces loudness in some areas and reinforcement that increases loudness in other areas. These interactions are also frequency dependent, so the character of the sound is also changed. The figure below shows sound scattering and diffusion in a simulated living room scene. The top row shows an empty room while the bottom row is fully-furnished. The left three columns show a 2D slice of the sound field generated by a Gaussian impulse emitted near the room’s center, while the right column shows the entire IR at a single receiver point placed at the source location. Red/blue represents positive/negative pressure in the sound field. Black areas represent solid geometry in the scene. Note the large difference in wave propagation in the two scenes because of scattering and diffraction.

Sound waves interact with room surfaces in fairly predictable ways.

Every room with walls and ceiling tends to resonate at certain frequencies that depend on the distances between the various reflecting surfaces. The mathematical equation used to calculate these frequencies is F = 1130/2D, where F is the Frequency in Hz (cycles per second) and D is the Distance in feet between two surfaces. The constant 1130 is the speed of sound at room temperature in feet per second, For example, a room that is 21 feet long will tend to have a resonance at 1130/42 = 27 Hz. This is the fundamental resonance for that mode, Depending upon the absorption characteristics of the room, it will also tend to oscillate or resonate at multiples of the fundamental frequency. For all practical purposes, any modal frequencies above 300Hz will be swamped by other room acoustic effects.

There will also be Nodes, or minimums at half the distance of the fundamental and other resonance frequencies. Note that such resonance modes will occur for all the primary surfaces of the room – front-back, side-side, floor-ceiling. These are called Axial modes. There are also tangential resonance modes involving four room surfaces, and oblique modes involving all six surfaces. These other room modes don't affect the sound as strongly as the axial ones, but all reflections affect the overall sound. The degree to which these resonance modes affect the sound depends on the absorptivity characteristics of the room and its furnishings. In his book on sound reproduction, Dr. Floyd E. Toole shows that a loudspeaker having a flat on-axis anechoic response will have a room curve that tilts downward with increasing frequency. This is why equalizing a system to a flat room curve results in a subjectively bright sound. It's somewhat disheartening how little this is understood. Further, In the modal frequency region of a room, the room itself dominates the system frequency response, so for optimum bass performance, room modes and their interaction with the loudspeakers and/or subwoofer(s) must be taken into account.

Andreas Melcher has a website that features a Room Mode Calculator that can be used to analyze a room given its dimensions, This is a fantastic tool that even lets you hear the sound of each resonance mode.

Control Options

An audio tech may not have the capability of modifying the acoustics of the venue where her/she is working, but knowing how room acoustics affects sound will help in determining what to do about the sound of a room. For example. some experienced audio techs actually measure the room spacings and calculate the primary resonance modes they expect to be produced so they know where they may need to apply appropriate EQ corrections. On the other hand, if working in a house of worship, there may be some things that can be done to modify the room acoustics, and if the venue is a home theater, there are more options available.

Acoustic Sciences Corporation has an excellent series of articles on Auditorium Acoustics by Acoustical Engineer Art Noxon. He says that Acoustics is not about the 1/10th of 1% of the sound from the loudspeaker that is directly heard by the people, but is about the other 99-9/10ths % of the sound from room surfaces. Perhaps he exaggerates, but room acoustics is very important to perceived sound. He also has a series on Home Theater Acoustics that is highly informative.

Acoustic Frontiers sells the XTZ Room Analyzer Pro app for PC that will help perform acoustic measurements in a room, This page is an excellent information source on the topic of room resonances. Has links to other resources,

The University of Southampton has several excellent pages of information on sound waves, with some nice animations of wave behavior,

Steve Kendig at Crutchfield has an excellent and extended article on room acoustics, how to calculate resonance modes, and how to deal with room resonances.

Floyd E. Toole has an excellent book entitled Sound Reproduction: The Acoustics and Psychoacoustics of Loudspeakers and Rooms. The author, a consultant for Harman and a Fellow of the AES, explains the physical and perceptual processes that are involved in sound reproduction and demonstrates how to use the processes to create high-quality listening experiences in stereo and multichannel formats.

Dr. J. Hunecke has an excellent set of pages that deal with room acoustics, resonance mode calculations, and a loudspeaker calculator that contains 37 generalized loudspeaker models derived from more than 650 real loudspeakers. While the assumptions used may not match your particular venue, the loudspeaker calculator can help analyze various parameters for controlling room acoustics,

SoundProfCOW specializes in various types of acoustic panels and sound absorbing materials, including a quick guide to soundproofing,

The Room Equalization Wizard REW is free room acoustics and audio device measurement and analysis software for room, loudspeaker and device responses. The audio measurement and analysis features of REW help you optimize the acoustics of your listening room, studio or home theater and find the best locations for your speakers, subwoofers and listening position.

TrueRTA's audio spectrum analyzer software shows you a detailed picture of what you're hearing in real-time. The Level 1 analyzer is free, but bandwidths are limited to one octave. The 1/3 Octave version is $40.

Hearing Protection Guide at Sweetwater shows how important it is to use hearing protection.

The physics of Reflection, Refraction, and Diffraction is discussed briefly at the Physics Classroom site.

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