Acoustics 101-Sound Basics
Front View Of My A/V Room Showing the Ceiling and Side First Point Reflection and Front Bass Absorbers
Introduction
This is the first of three posts that will look at:
- Sound, what it is and some important parameters.
- The room, how to absorb sound and the correct placement of absorption and subs.
- How to design and make sound absorbers.
You don’t need to have amazing acoustics and carpentry skills and buckets of cash to significantly improve your rooms acoustics. It can also often be accomplished without causing too much friction with your partner.
Basic acoustics and the way it can impact your sound are not difficult to understand. Once you have grasped the fundamentals of how sound is transmitted around a room and how to control that transmission with absorbers and diffusers, you can make big improvements to your rooms sound.
This series of posts is only meant to enlighten the reader into understanding some of the basics into effectively treating the acoustics of a room. It is not a detailed introduction into designing your own Home Theater. Details for such a project can be found here. There is a lot that electronic equalization cannot do, do well or do at all, and basic good room acoustics is always a pre-requisite for getting a good sound.
These posts deliberately contain little math, and on occasions take a few technical liberties in the interest of keeping things simple.
What Is Sound?
Sound is nothing more than the compression and expansion (rarefaction) of a materials (mediums) molecules. For air, at 68 degrees Fahrenheit, this increase and decrease in air pressure moves through it at approximately 1125 ft/sec or 343 m/s. This velocity falls at lower temperatures and rises at higher temperatures.
Sound can travel through all mediums except a vacuum, (in which there are no molecules), where sound cannot travel at all. That’s why “nobody can hear you scream in space”! The medium or material that the sound travels through impacts its speed. The more elastic and denser the material the faster the sound wave travels or propagates. For example, the compression and rarefaction of steel molecules when you strike a steel bar moves through it at approximately 15,000 ft/sec, through water its 4,700ft/sec.
We are mainly concerned with the transmission of sound through air, so all other materials will be ignored for now.
For the Audiophile, this moving air pressure wave contains energy that was put there by typically a speaker, but any source that can compress and rarify air in contact with it transfers energy to the air, your vocal chords for example.
Transmission of Sound
The sound energy doesn’t leave, or radiate from the source in a straight beam like a search light. It spreads out in a spherical manner radiating in all directions depending upon the source design.
Theoretical Point Source Sound Radiation
Sound Radiation From A Speaker
This moving pressure wave posses two important properties that, as will be seen later, affects how we can absorb it.
- At the points of maximum compression and rarefaction the air has no velocity but has maximum or minimum pressure
- As the pressure wave crosses from compression to rarefaction and back it has the same air pressure as that of the environment through which it passes, but maximum velocity.
Air Pressure and Air Velocity
Sound Pressure Measurement
Sound pressure is measured in Pascals (Pa). In practice Pascals are rarley used to describe sound pressure, and most sound pressures are referenced to a known standard of 20 micro Pascals. This level corresponds to the threshold of hearing of a typical young healthy ear. Due to the response of the ear, a logarithmic scale is used to describe the percieved sound pressure level (SPL). The mathematical formula is SPL = 20log (P1/P0) decibels, where P1 is the actual pressure and P0 is the known standard, both in Pascals. This formula creates ratios of how loud the sound is relative to the reference in Decibels (dB). A +6dB increase means the SPL doubles, a -6dB change means thats the SPL halved. Speech is typically at a +70dB level. See the Equal Loudness Contours below for typical dB levels.
Frequency and Wavelength
The rate at which the compression and rarefaction of the air occurs is called its frequency and is measured in cycles per second or Hertz (Hz). For a simple pure tone (sine wave), a complete cycle or Hz, would be from one point on the sine wave to the next identical corresponding point, encompassing one compression and one rarefaction.
Most humans can hear from 20Hz to 20,000Hz. However, our ears are not equally sensitive to all frequencies, see below.
Equal Loudness Contours
Our ears are most sensitive to frequencies around 4000Hz and become increasingly less sensitive to frequencies below 200Hz and above 15,000Hz. We see why at bass frequencies below 80Hz why such huge speakers and powers are required in order to create sound pressures that are perceived by the listener as being the same as those in the higher frequency ranges.
If a sound wave has a frequency, and it moves through a medium, then it must have a length that each cycle or Hertz occupies. This distance is called its wavelength.
The frequency (F) of a sound in Hertz can be related to its wavelength – lambda (ƛ) in feet and the speed of sound (S) in feet/s using this simple formula:
S=F*ƛ or 1125=Frequency*Wavelength
As an example, a 1000 Hz tone would have a wavelength of 1125/1000 feet = 1.125 feet, a 100Hz tone would have a wavelength of 11.25 feet and a 10Hz tone would have a wavelength of 112.5 feet
Wavelength of a 1KHz Tone
Angular Measurement (Phase)
A single wavelength of a sound wave is said to occupy 360 degrees. So, if we look at a pure tone sine wave we get the following angular assignments.
Waveform Phase Angles – Air Pressure
These angles are important as they relate to the level of the air pressure, or velocity, along the sound wave. In this diagram at 0, 180 and 360 degrees there are no changes to the air pressure. At 90 and 270 degrees the air pressure is a maximum and minimum respectively.
These angular measurements are often used to describe the time relationship between two or more waveforms. This is where the term Phase arises. See the following examples:
Phase Angles
Relative to waveform C:
- E is 180 degrees phase delayed or phase inverted.
- D is 90 degrees phase delayed.
- B is 90 degrees phase advanced.
- A is 180 degrees phase advanced or phase inverted.
Volume (loudness)
The volume of sound simply relates to how much the air is compressed and rarefied, or how much energy the medium (air) is carrying.
Sound Volume – Waveform A Is Louder Than Waveform B
Sound Composition
It can be shown that any repetitive sound can be broken down into a series of pure tones or sinewaves of different frequency, amplitude and phase (A Fourier Analysis). The simplest example of this is a the square wave. This is composed of a base frequency sine wave called its fundamental and in theory an infinite number of odd numbered multiples of that fundamental frequency called its harmonics.
Square Wave Analysis
We shall only be discussing sine waves as they behave acoustically in the same way as complex musical waveforms.
Reflection and Diffusion
When sound strikes a flat surface, it is uniformly reflected by that surface at the same angle that it strikes it at. The angle it strikes it at is the angle of incidence, the angle it is reflected at is the angle of reflection and they are equal.
Sound Reflection Off A Smooth Surface
If the surface is uneven the sound wave will break up and be reflected at different angles, an effect called diffusion. The degree and type of diffusion depends upon the design of the surface. It also depends upon the frequency (wavelength) of the incident sound wave. The lower the frequency and the longer the wavelength the more ineffective this effect becomes. Diffusing low frequencies requires very large and sometimes quite complex structures and is generally not done.
Sound Reflection Off An Irregular Surface
The control of these surface reflections is very important to overall sound quality, including image and depth perspectives. These will be examined in more detail in the next post.
Flutter Echo
This effect is produced usually by parallel reflective surfaces. It is the fast discrete repetition of a sound as it bounces between the surfaces. Stopping this problem is very easy, by simply adding small patches of absorber, diffusers or angled reflection surfaces.
Flutter Echos
Comb Filtering
This audible effect is created when the path length between two identical sounds is typically less than 10mS. It causes the mid and high band frequencies within the combined sound to interfere with each other and go in and out of phase, creating a frequency response that looks like the teeth on a comb. It produces a hollow distinctive sound as various mid and high frequencies are boosted and cancelled. This effect is often used in popular recordings and generated electronically where it is called phasing or flanging, producing a ‘whooshing’ sound. First used to great effect, I believe, on Itchycoo Park by the Small Faces in 1967.
In typical listening rooms and home theaters this effect is rarely heard due to the large number of different path lengths created by the rooms many reflections. These cause numerous comb filter effects that hopefully average out to a flat frequency response.
Typical Comb Filtering Frequency Response
Sound Energy Absorption
The energy contained in a sound wave will be dissipated or absorbed by the medium it travels through or it can be absorbed when it strikes an object. This absorption can ONLY take place by turning the sound energy into heat. (Electronic sound pressure cancellation is not considered in these posts.)
In all cases of sound absorption, the movement of the molecules that carry the energy is absorbed by the medium through which it passes and/or strikes. This process of absorption is exclusively carried out by converting the molecular movement/sound energy to heat energy. Eventually, given enough of the medium, all the sound in it will be absorbed by it as heat. Sound doesn’t travel forever. Fast, efficient absorption of the energy from air requires that the energy from its movement be transferred to another material that will convert it to heat. So, the air pressure needs to cause some other material to vibrate and internally create heat from friction, causing the air to give up its sound energy. Just like two sticks rubbed together can cause enough heat to ignite them. We need the ‘sticks’ or fibers to be rubbed together or cause another material to be vibrated by the air pressure changes. In the case of sound, the energy levels and therefore heat generated are very small, so NO flames!
Sound Decay
If sound is being absorbed by being turned into heat then its level must be decaying with time. The rate of decay is VERY important as it really impacts what a room sounds like. Much research has gone into optimal decay times for different sized rooms and what they are being used for in order to optimize the sound listening experience. All the way from huge concert halls and studios to small recording, TV and radio control rooms.
Sounds in a room are not singular in that they contain many many frequencies and thousands of reflections of many surfaces. This mixture of sound energy is referred to as a sound field and as perviously stated decays with time. The length of time that the decaying sound field can be heard for is known as the rooms reverberation time. It is defined as the time taken for the sound to decay by 60dB (RT60 or T60) or to 1/000th of the level of the original direct sound. Measuring a decay of 60dB is often impractical due to a number of reasons, so decays of 10dB (T10), 20dB (T20) and 30dB (T30) are often taken and then extrapolated to provide a T60 decay time.
Reverberation Time RT60
My A/V Room Reverberation Decay Curves for T10, T20 and T30
We see that the calculated T10, T20 and T30 decays are all approximately 0.2 seconds. In reality, and by design, my room decay is slightly shorter than 0.2 seconds.
For high quality analytical home listening we should be aiming for a UNIFORM decay time of ALL frequencies of approximately 0.2-0.3 seconds but certainly no longer than 0.4-0.5 seconds. While this is quite achievable above the rooms Schroeder Frequency of about 100Hz -200Hz (for typical household rooms), achieving it at frequencies below 100Hz can be very challenging, requiring large absorbers and good room design.
NOTE: A rooms Schroeder frequency is really a range of frequencies above which the decay of the sound is governed by room reflections (ray behavior) as the sound bounces all around the room and below which the decay of the sound is governed by standing waves (room modes).
My A/V Room Front L/R Speakers Frequency Response
The center Schroeder frequency (Fc) for a given room maybe calculated using:
Fc = 2000 x square root(RT60/V) Hz
Where RT60 is in seconds and (V) is the volume of the room in cubic meters. For My A/V Room Fc =2000 x sq.rt.(0.2/53) = 122Hz
Optimal decay times vary significantly based upon the size of the room and its use. Concert halls may be as long as several seconds where as small control rooms, home theaters and typical residential rooms are typically 0.2-0.5 seconds, which is what we are concerned with. Generally speaking the smaller the room the shorter its decay needs to be to make the sound intelligible. Very fast decays above 200Hz of 0.1 seconds will cause rooms to sound dead and lifeless, where as long decays of 0.5 seconds and up can cause the sounds to become muddled and indistinct particularly at frequencies below 80Hz where the bass will become muddy, boomy and colored.
A rooms reverberation time is easily measured these days using inexpensive applications that can run on PC’s and iPhones and may be calculated at a simplistic level using Sabine’s formula:
RT60= 0.05.(V/S.a) seconds.
Where (V) is the volume of the room in cubic feet, (S) is the surface area of the absorption in square feet and (a) is either the rooms average absorption coefficient per square foot or absorption coefficient per square foot at a particular frequency.
A Typical Bass Waterfall Graph
A waterfall graph is one way that we can see how sound decays at each frequency in a room. In the above graph sounds above 20Hz decay by 30dB in approximately 0.2 seconds with the longest low frequency decay time of approximately 0.3 seconds. It should also be noted that the rooms bass frequency response is reasonably flat. Fast decay and flat frequency response will help ensure a relatively neutral sounding room with tight and clean bass.
Achieving the ideal goal of a uniform frequency room decay requires careful deployment and selection of absorbers, careful room equalization and often additional subs.
Standing or Stationary Waves – Room Modes
A standing wave pattern is created when two sound waves of the same frequency collide or interfere with each other. They occur at specific frequencies based upon the dimensions of a room and are created by the sound waves being repeatedly reflected between surfaces. (Do not confuse with Flutter Echo which is a discrete echo of the sound as it bounces between parallel surfaces). This interference between the incident and reflected waves occurs in such a manner that the waves pressure maxima and minima appear stationary within the room. The points of maximum pressure amplitude are called antinodes, the points of minimum pressure amplitude are called nodes.
Standing waves can occur on any dimension of a room when its dimension is a multiple of half the wavelength of the associated frequency. Axial Modes are the easiest to understand and are formed on the rooms:
- Length
- Height
- Width
Room Axial Modes
If we just consider Axial room modes for simplicity, then at a boundary like a wall, where a sound wave gets reflected, the air pressure is at a maximum (antinode) and there can therefore be no air movement (node). For two parallel walls the lowest frequency that the room can create an Axial standing wave for would be a pressure maximum at each wall and a pressure minimum between them as shown below.
Lowest Standing Wave Frequency
We see that the lowest Axial frequency that a standing wave can be created for has a wavelength double that of the rooms longest dimension. So for my A/V room with a length of 18’6″, the lowest frequency would have a wavelength of (2×18’6″) = 37′ and a frequency of 30.4Hz.
As a 2nd example, a room whose length is 20 feet would have its Fundamental, first, or lowest frequency AXIAL standing wave at (1125/2*20) = 28.125Hz. The second standing wave would be 56.25Hz, the third would be 84.375Hz etc. Those frequencies above the Fundamental that generate standing waves are referred to as Harmonics.
There are some more complex standing waves that also occur when the sound wave bounces of several surfaces to include:
- Tangential
- Oblique
Additional Room Modes
These more complex modes can be easily calculated with a number of readily available simple and free programs – see below.
NOTE: The term antinode is used to denote a maxima and the term node is used to denote a minima. So care has to be taken as to wether you are discussing wave pressure or wave velocity, as their nodes and antinodes are opposite to each other; see below:
Sound Waveform Nodes and Anti-Nodes
For my A/V room with dimensions of 18′ 6″x12’8″x8’0″ the following graphs show the placement and frequency of the pressure standing waves. They also show the node distances (ft) from one surface of the room.
My A/V Room Standing Waves and Pressure Antinodes and Nodes
There are many programs that help calculate all the standing wave frequencies for a rectangular room. See the following links:
Calculating the modes for irregular shaped rooms is more complex and often requires specialist software.
Here is a combined view of the Axial, Tangential and Oblique modes for my A/V Room.
My A/V Room Modes – Note the minimal bunching at any one frequency and the fairly even spread of all modal frequencies.
At frequencies above about 300Hz, standing waves are not a problem and absorption is straightforward, as will be seen in post 2. However, at bass frequencies they become increasingly problematic as the frequency of the sound wave gets lower and its wavelength longer, making them increasingly difficult to absorb. It is these standing waves that give rise to a rooms uneven and often poor bass response. So clearly we will need a way to absorb/control the bass energy that creates them and bring them to a level where either they are barely audible or the systems electronic equalization and/or the addition of more subs can make up for their impacts.
Close examination of the above waterfall graph shows decay ridges at frequencies that coincide with those shown in the room mode frequency charts above. The lowest Axial mode being 31Hz. (I comment on the longer 15Hz decay in post 2)
In reality a standing wave is an interference phenomenon and NOT a wave at all. It is a pressure pattern caused by two sound waves of the same frequency moving in different directions and interfering with each other in the same medium.
These pressure maxima, and minima, are real, and give rise to fixed points in the room where certain bass frequencies are predominantly loud (antinode), or barely audible (node). As there are so many standing wave frequencies for a typical room, the one thing you DO NOT want to occur is to have the same standing wave frequencies created on each room dimension and for all three standing wave types. Should this occur they will become additive and the room can become very boomy and unpleasant at those frequencies. Their prevention is one of the most challenging issues in treating a room to create an even and smooth bass response. This is where your room dimensions and where you sit become very important. More on this in the next post.
However, there are still more issues to consider to a rooms acoustics like controlling reflections. These will be discussed in the next post.
What’s Next?
So now we know what sound is, its basic parameters, how it is to be absorbed and decays and most importantly, what a standing wave is.
In part two we shall look at:
- Common absorption Materials
- Room dimensions and the main listening position (MLP).
- Room dimensions and reflections.
- Types of absorbers, diffusers and their placement.
- Subs and their optimal placement – a basic introduction.
Click here for post 2 of this series: Acoustics 101 – Absorbers, Diffusers, Reflections, Room Dimensions and Subs.
Click here for post 3 of this series: Acoustics 101 – Designing Porous, Resonant and Reflective Sound Treatments.
For a great beginners introduction to acoustics see this Master Handbook of Acoustics.
For part one of the construction and acoustics details for my AV room click here.
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