Re: DIY Room Acoustics for Home-Theatre
Before reading this please ensure that you have enough caffeine (coffee) stocked near you...
Never read it a fast pace..Re-read it to understand concepts...Take time to understand the science behind acoustics..It is not rocket science..Just basic physics at work..This article is extracted statements from articles after reading books and articles by acoustic experts...
source:
Article by Big Daddy from http://forum.blu-ray.com/showthread.php?t=48286
www.acoustics.salford.ac.uk
http://hyperphysics.phy-astr.gsu.edu
and other books by renowned acoustic experts...
I have simplified it further so that the concept can be understood by newbies like me..Happy reading...
Disclaimer:
I am not responsible or liable for causing headache, due to aching brain (information overload)
What is sound:
Sound is a wave that travels through matter such as air, water, and steel. Sound does not travel in vacuum. A sound wave will spread out after it leaves its source, decreasing its
amplitude or loudness. A single- frequency traveling wave will take the form of a sine wave.
The speed of sound in dry air is approximately 344 meters/second, 1127 feet/second. Sound travels faster in liquids and non-porous solids than it does in air, traveling about 4.4 times faster in water than in air. The speed of sound in air varies with the temperature and humidity such that sound travels slower on cold days, but is nearly independent of pressure.
Sound waves are an example of longitudinal motion. View air getting displaced:
Formation of Standing Waves:
Sound reflects back and forth between two parallel surfaces.
At certain frequencies the incident and the reflected sounds interfere to form standing waves in which those frequencies can be amplified. Hence a standing wave pattern is an interference phenomenon.
It is formed as the result of the perfectly timed interference of two waves passing through the same medium. A standing wave pattern is not actually a wave; rather it is the pattern resulting from the presence of two waves of the same frequency with different directions of travel within the same medium.
Read further and you will understand it better
Let's start by putting just one sine-wave into the left-hand end of the string, and allowing it to travel towards the reflecting boundary.
[IMG2]http://www.acoustics.salford.ac.uk/feschools/waves/flash/string2.swf[/IMG2]
In the animation, there is a attempt to show that when the wave is reflected, there is a phase change - if the displacement of the string is in an 'upwards' direction for the wave travelling left-right, then the reflected wave will be displaced in a downwards direction. This means that sine waves are continuously travelling from left to right, changing phase by 180 degrees on reflection, and travelling back from right to left. The incident and reflected waves interfere with each other by superposition and the following pattern results:
http://www.acoustics.salford.ac.uk/feschools/waves/flash/string3.swf (open flash animation in new tab in your browser)
The composite waveform is known as a standing wave. It differs from a travelling wave (transverse or longitudinal - in fact every type of wave we have considered so far has been 'travelling') since the pattern oscillates, but appears to be stationary - there is no apparent right-left or left-right movement of energy. Every standing wave has
nodes (locations of minimum amplitude) and
antinodes (locations of maximum amplitude).
Hey, what are these Nodes and Anti-nodes stuff ???
One characteristic of every standing wave pattern is that there are points along the medium that appear to be standing still. These points, sometimes described as points of no displacement, are referred to as nodes.
There are other points along the medium that undergo vibrations between a large positive and large negative displacement. These are the points that undergo the maximum displacement during each vibrational cycle of the standing wave. In a sense, these points are the opposite of nodes, and so they are called antinodes.
A standing wave pattern always consists of an alternating pattern of nodes and antinodes.
The positioning of the nodes and antinodes in a standing wave pattern can be explained by focusing on the interference of the two waves. The nodes are produced at locations where
destructive interference occurs. For instance,
nodes form at locations where a crest of one wave meets a trough of a second wave; or a half-crest of one wave meets a half-trough of a second wave; or a quarter-crest of one wave meets a quarter-trough of a second wave; etc.
Antinodes, on the other hand, are produced at locations where
constructive interference occurs. For instance, if a crest of one wave meets a crest of a second wave, a point of large positive displacement results. Similarly,
if a trough of one wave meets a trough of a second wave, a point of large negative displacement results. Antinodes are always vibrating back and forth between these points of large positive and large negative displacement; this is because during a complete cycle of vibration, a crest will meet a crest; and then one-half cycle later, a trough will meet a trough. Because antinodes are vibrating back and forth between a large positive and large negative displacement, a diagram of a standing wave is sometimes depicted by drawing the shape of the medium at an instant in time and at an instant one-half vibrational cycle later.
HeY...I am confused ???? :sad:
Read further
..and you will understand it better..and re-read it again
A node is a point along a standing wave where the wave has minimal amplitude. The opposite of a node is an
antinode, a point where the amplitude of the standing wave is a maximum. These occur midway between the nodes.
Nodes and antinodes should not be confused with crests and troughs. When the motion of a traveling wave is discussed, it is customary to refer to a point of large maximum displacement as a crest and a point of large negative displacement as a trough. These represent points of the disturbance that travel from one location to another through the medium. An antinode on the other hand is a point on the medium that is staying in the same location. Furthermore, an antinode vibrates back and forth between a large upward and a large downward displacement. And finally, nodes and antinodes are not actually part of a wave. Recall that a standing wave is not actually a wave but rather a pattern that results from the interference of two or more waves. Since a standing wave is not technically a wave, an antinode is not technically a point on a wave. The nodes and antinodes are merely unique points on the medium that make up the wave pattern.
I am a newbie..what is amplitude ??:indifferent14:
Amplitude is the measure of the amount of energy in a sound wave.
So the greater the intensity of a sound, the greater the amplitude.
Fundamental frequency and harmonics:
We know that what we hear as a single sound or pitch when someone is speaking is really a fundamental frequency (determined by how many times the vocal folds vibrate in one second, and measured in cycles per second [cps], or Hertz.
The frequency which drives the lowest standing wave is the fundamental frequency.
http://www.acoustics.salford.ac.uk/feschools/waves/flash/string4.swf
if we vibrate the string twice as fast and assume that the speed of the wave, and thus the time taken to travel 'there and back', do NOT change, then by the time the wave gets back to the start the shaker will have completed two complete oscillations...but exactly two. This means that the returning wave still arrives at just the right 'point-in-phase' - and so interferes constructively with the next wave sent out. Another standing wave results:
http://www.acoustics.salford.ac.uk/feschools/waves/flash/string5.swf
The same rules apply if the string is vibrated 3, 4, 5 etc times as fast, as the fundamental case.
Because the standing waves occur at integer (whole-number) multiples of the fundamental frequency, they are sometimes called harmonics.
The harmonics are multiples of the fundamental frequency. So if the fundamental frequency is 100 Hz, the harmonics will be 200 Hz, 300 Hz, 400 Hz, 500 Hz, and so on. If the fundamental frequency were 220 Hz, the harmonics would be 440 Hz, 660 Hz, 880 Hz, and so on.
The animation below shows the first four harmonics of a string simultaneously:
http://www.acoustics.salford.ac.uk/feschools/waves/flash/string8.swf
Musicians prefer the term overtones and physicists prefer the harmonic term.
Harmonics and overtones are also called
resonant frequencies.
SUBWOOFERS AND THE EFFECT OF STANDING WAVES:
Low frequency wavelengths are much longer (e.g., 56.5ft at 20Hz, 22.6ft at 50Hz, and 11.3ft at 100Hz) than higher frequency wavelengths (e.g., 3.8ft at 300Hz, 1.1ft at 1,000Hz, and 1 inch at 13,000Hz). This is important, especially below 150hz or so. Above 150hz, the waves are small enough that they are not affected by the room size as much. They bounce around every which way. Standing waves only become a significant problem at lower frequencies (below 100 Hz) because we normally set the crossover frequency around 85Hz.
Oh! what is this crossover stuff ??
Crossovers split the audio signal into separate frequency bands that can be separately routed to loudspeakers optimized for those bands.. In a home theater set up (5.1, the .1 being the sub-woofer) the amp will usually have a crossover setting. Assuming all speakers as set to 'small' then all frequencies below the crossover (usually around 80Hz) are sent to the sub-woofer, and all frequencies above sent to the remaining speakers.
In general, at most frequencies, the decay of sound waves is rapid, but when a sounds wavelength is precisely twice the size of a room dimension (e.g., length), the waves from both directions reinforce each other at the wall boundaries and cancel each other in the midpoint of these two boundaries, creating a resonant condition. Like most other resonant conditions,
standing waves produce a fundamental tone (the lowest-frequency resonance the space will support) and a series of harmonics.
Standing waves in a room are called room modes or room resonance modes.
Type of Room Modes:
The sound waves interact with the room boundaries (walls, floor, and ceiling) and create standing waves or room modes. The standing waves are different between floor and ceiling, side walls, and end walls, unless any of these dimensions are the same (the worst kind of room is a perfect cube). There are three basic types of modes: axial, tangential, and oblique.
To gain some understanding of the room modes and standing waves, it will be very helpful to consider a one-dimensional acoustic space like a long narrow pipe. If both ends of the pipe are closed, then it becomes similar to a one-dimensional room.
Now position a sub-woofer at one end of the pipe and connect it to a frequency generator. At the other end of the long pipe, put an SPL meter to measure the sound pressure. Start by feeding very low frequency signals to the subwoofer, you will notice no reading on the SPL meter. However, as you increase the frequency of the sound waves fed to the sub-woofer, you will reach a point where the reading on the SPL meter jumps to a high point. This is the first mode and is called the fundamental resonant frequency or the first harmonic frequency of the one-dimensional room (pipe).
Continue raising the frequency of the signals and the meter drops back to normal for a while, but finally peaks again. This next frequency is evidence of the second resonance mode and is called the second harmonic frequency. The frequency of this second resonance will be exactly twice that of the first resonance. If we increase the frequency of the signal some more, we will find the third resonance mode which will have exactly three times the frequency of the first fundamental resonance mode. This harmonic series can continue as we increase the frequency.
In a closed pipe, which has been stimulated into its first resonance condition, we will find that the sound is very loud at either end of the pipe and very quiet at the halfway point, the middle. These loud areas are called sound pressure zones.
If the sub-woofer is placed in either of these pressure zones, it can pump up the resonant condition. However, if it is not placed in a pressure zone, it cannot pump up the resonant mode.
The second harmonic of a closed pipe has three pressure zones, one at either end and one in the
middle. If we place the sub-woofer in any three of these pressure zones, we will stimulate the second harmonic. However, if we place the subwoofer in the middle pressure zone, we cannot stimulate the first resonance but we can still stimulate the second one. Let us now plot the sound pressure as a function of distance, and remember that one wave moves from left to right and the other moves from right to left and polarity changes each time we cross a null.
Important Facts About Subwoofers, Listeners, and Standing Waves
Sub-woofers are sound pressure generators.
They will reinforce the room modes when they are located in high pressure regions of the standing waves.
If the sub-woofer is placed in the null areas, the corresponding modes will disappear.
The pressure zones are spread out and not pinpoint-sized.
For all practical purposes, the sub-woofer should be located at least 25 percent away from the end of the pipe to best avoid stimulating any of its first three harmonics. There is no location towards the middle of the pipe that suits a sub-woofer position, as the pressure zones there are overlapping.
Calculating the Resonance Modes of a Home Theater Room and Sub-woofer Placement:
Axial Modes are the strongest and the most important, and the easiest to compute. A room can be approximated by three intersecting pipes. These pipes would lie along the three room axes: front to back, side to side, and floor to ceiling. For most rectangular home theater rooms, it may be sufficient to calculate only the axial modes of the room.
Since a room can enforce a wave twice as long as it is, the first fundamental frequency can be calculated by using the formula:
Standing Wave Frequency = Speed of Sound / 2*Distance Between Boundaries.
If we multiply this frequency by 2, we will get the second harmonic frequency and so on. Usually it is necessary only to look at the first three or four modes because the crossover frequency for most home theater rooms are set around 80Hz-100Hz.
Let us now calculate the axial modes for a 15ft W x 20ft L x 8ft H room.
Width:
The first resonance frequency: 1130ftps / 2x15ft = 37.7Hz. (1130 ft/s is speed of sound in air)
The second resonance frequency: 37.7 x 2 = 75.4HZ.
The third resonance frequency: 37.7 x 3 = 113.1HZ, ignore, because it is above the roll-off frequency of 85Hz.
The sub-woofer has to be placed at least 25 percent away from the wall (15x0.25=3.75ft) because of the first harmonic, but that is the point of minimum of the second harmonic. Therefore, the sub-woofer can be placed anywhere between 3.75ft (minimum of the second harmonic) and 7.5ft (minimum of the first harmonic) away from either wall.
Length:
The first resonance frequency: 1130ftps / 2x20ft = 28.3Hz.
The second resonance frequency: 28.3 x 2 = 56.6HZ.
The third resonance frequency: 28.3 x 3 = 84.9HZ.
Since all three harmonics are below the roll-off frequency of 85Hz, we should place the subwoofer in a position that avoids the maximum and minimum of the three waves at least 25% (20 x0.25=5ft) from either end walls.
Height:
The first resonance frequency: 1130ftps / 2x8ft = 70.6Hz.
The second resonance frequency: 70.6 x 2 = 141.2HZ, ignore, because it is above the roll-off frequency of 85Hz.
The third resonance frequency: 70.6 x 3 = 211.8HZ, ignore, because it is above the roll-off frequency of 85Hz.
The vertical position for a subwoofer is anywhere in the middle half of the room, keeping it at least 25% (two) feet away from either the floor or ceiling.
So, a 15ft W x 20ft L x 8ft H room will have the smoothest bass if the subwoofer is located 2ft from the floor or 2ft from the ceiling (6ft from the floor), between 3.75ft and 7.5ft from the side walls, and five feet from the end walls.
This is done to avoid the coupling of the subwoofer to room modes.
Dr. Floyd Toole, formerly of National Research Council of Canada and currently a Vice President and researcher at Harmon International has developed a simple Excel Program to calculate axial room modal frequencies.
http://www.harman.com/EN-US/OurCompany/Innovation/Documents/Calculators/Room Mode Calculator.xls
Just change the room width, length and height in the excel sheet and you will get the updated room modes..
The following analysis is based on the work of Dr. Floyd Toole.
One Sub-woofer
Let us consider the width modes. One sub-woofer close to a wall is in the high pressure region of all the width modes and energizes all of them.
What happens if the sub-woofer is moved to the location of the first pressure minimum (green minimum)? That particular mode is not energized and will disappear. What then happens if it is moved to the next null (magenta minimum)? That mode will disappears, but the other one returns.
Sub-woofer location determines which of the room resonances is activated, and which ones are not activated.
Optimum Position for One Sub-woofer:
If the sub-woofer is placed in the wrong position in the room, we hear
room booms instead of music. Bad speaker positions are those that allow the speaker to stimulate room resonance (modes).
In a square or rectangular room, the center of the room is the worst location for the listening chair or for the subwoofer
Rule of 25:
The low frequency sound waves generated by sub-woofers interact with room boundaries and create standing waves (pressure zones). These pressure zones are spread out and not pinpoint-sized. For all practical purposes, the sub-woofer should be located at least 25 percent away from the room boundaries to best avoid stimulating any of its first three harmonics. There is no location towards the middle of the room that suits a sub woofer position, as the pressure zones there are overlapping.
This solution is suggested by Todd Welti at Harman International:
You shrink the whole room by 25% and put the subwoofers at the corners of that virtual room. Of course you get incredible performance, but that is not practical for most people. But if you use two or four subwoofers in the corners or the wall midpoints, you can get pretty good performance.
Room Modes (
Additional Reference)
http://gikacoustics.com/what-are-room-modes/
