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Tuesday, October 02, 2012

Does More Speakers = More Volume Pt. 1 (Background

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if you are interested in skipping this background info and get to the heart of the subject then here is the link for the 2nd blog:

http://profile.ultimate-guitar.com/gumbilicious/bl og/110903/

The purpose of this blog is to shed a bit of light on an issue that gets brought up time and time again: “Does More Speakers Equal More Volume”.  At first, I thought this was a pretty open and shut case, but after some time I realized there is more to this problem than the surface arguments.  For those who are not familiar with the debate, I will summarize the two most popular sides:

Side A: adding an extra speaker gives a +3 dB boost over using a single speaker because two speakers push more air than one speaker

Side B: no matter many speakers you run, the law of conservation of energy must hold, and there should be no increase in output just by adding speakers to the circuit.

By the way, I was firmly entrenched with Side B, I took enough physics in school to know that you can’t violate conservation laws.  What I have found is that both sides aren’t really right, not because they aren’t both partially right.  Each side has a bit of truth, but both sides simplify the problem too much to be conclusive.

In order to understand what is going on here, we are going to have to get a bit technical.  We are going to have to know what harmonics are, some basic wave mechanics, and even get into idealized thought experiments.  So let’s get started.

What is Sound?


Sound is basically air moving, usually a systematic increase and decrease of air pressure.  In our musical world, we can think of an object moving which causes the air to move around it.  Think of an object moving back and forth, when the object moves forward it compresses the air in front of it and then when it moves back it rarefies the air in front of it.  This creates a series of higher and lower pressures, which can be represented as a sine wave.

For the sake of saving time, here is a link with pictures and a better explanation of the basics of sound.

http://en.wikipedia.org/wiki/Sound

So the simplest sound can be represented as a sine wave that has an amplitude (how loud it is, aka: it’s intensity) and a wavelength (this corresponds to the frequency).  But real world noises, including most instruments we play, don’t produce ‘simple sounds’.  Real sounds we encounter are not made of one single frequency, instead they are made by multiple frequencies interacting with one another.

When we talk about more complicated sounds, with multiple frequencies interacting, then we refer to the lowest frequency in the sound as the ‘fundamental’ while the higher frequencies are called ‘harmonics’.  Technically even the fundamental is a harmonic, it’s called the ‘first harmonic’; the next highest frequency is called the ‘second harmonic’; the third highest frequency is called the ‘third harmonic’, etc.  Here is another link with graphics:

http://en.wikipedia.org/wiki/Harmonics

Now, each one of these harmonics can be considered a sine wave in and of itself, it just so happens to interact with other frequencies and when you add these sine waves together you get waves that look nothing like a sine wave.  Here is a link with some good pictures so you can get the gist

http://www.acs.psu.edu/drussell/demos/superpositio n/superposition.html

Why do I mention all of this?  Well it is important for you to know about a simple sound of just a pure sine wave as we will be using that in our thought experiments.  It is also important for you to understand that real sounds (like notes on a guitar) are made of multiple sine waves summed together because that will be important in appreciating real world complexities.  We will also be dealing with waves interfering with one another, so it is important to understand how waves can interact with each other.

The Near Field

Very briefly, let us review what a near field is because it is an important concept in our thought experiments.  The near field represents an ideal listening environment, absent of any surfaces or imperfections that may reflect or interfere at all with our listening experience.  When we invoke the near field in a thought experiment, then will consider no reflections or wave interference at all.  You can think of a near field as floating in the sky, far away from any object, so that all we hear is sound from the source signal exactly as it is reproduced.

It is important to realize a near field is impossible to achieve.  In real life you will have to deal with the environment and it’s impact on sound, but the near field is a useful concept to help us simplify a thought experiment so that we pay attention to the concept we are trying to understand without compounding complications.

All of our calculations are going to assume a near field.

http://www.icad.org/websiteV2.0/Conferences/ICAD96 /proc96/brungart.htm

Sound Perception


It is important to note a few things about how humans hear noise.  First off, we can hear a very large range of loudness/volume (represented by the amplitude of the sound wave) and we call this range of loudness that we hear ‘Dynamic Range’.  For example: if we are at a very loud rock concert that pushes the limits of the loudness our ears can handle, we can also distinguish a noise with an amplitude 100,000 times less than the rock concert (not at the same time though).  That is pretty impressive, and it also leads to problems in representing numbers because they can end up becoming HUGE when we make comparisons.  Because the dynamic range of our hearing is so big, we actually adopt a logarithmic scale called the decibel scale.  The benefit of doing this is that numbers in decibel form remain small and easy to manipulate even when differences in sound are huge.

http://en.wikipedia.org/wiki/Dynamic_range

Another thing to briefly mention is that humans also have quite a large range of wavelengths or frequencies of sound we can hear.  Humans can hear sounds from 20 Hz to 20,000 Hz.  Just as importantly, a human’s ears do not treat all frequencies equally.  Some frequencies (around ~1,000 Hz) sound louder to us than all the other frequencies, because our ear is more sensitive in this range.

http://en.wikipedia.org/wiki/Loudness

Sound Power vs Sound Pressure

This is a confusing topic surrounding sound that we will try to address and clear up.  Sound power represents the amount of sound energy a source radiates directly, the sound power does not take into consideration environmental factors at all.  Sound pressure on the other hand is how the radiated sound interacts with the environment and is indicative of what our ears actually hear.

To give a more tangible example, let us compare sound to heat.  A heater has a certain rating for output (btu or watt) that represents the intensity of the energy output of the device.  But if someone is standing in a room with the heat source and you ask them “How hot is it in here?” their answer will most likely not match the output of the heat device exactly.

The reason for this difference in device output and perceived temperature has much to do with heat’s interaction with the environment.  

-    Heat will be the most intense nearest the heating device, as you approach the heating device you will feel more heat.
-    Heat distributes itself throughout the room, when you first turn on a heating device in a cold room it will take some time for the whole room to warm up.
-    The shape of the room will come into play as to where the hotter air will end up, for example: a room with tall ceilings will take longer to heat because heat rises.
-    The size of the room has to be considered when figuring out how long the room will take to heat up and what temperature the room will reach.

These factors all determine the temperature of the room and explain how a room may feel cold even though you have a heater with immense output.

Similarly, sound power can be compared to the output of the heater and sound pressure is analogous to room temperature.  When we measure sound power output of a speaker it may not match entirely with the perceived volume in a room.

-    Loudness should be the most intense the closer you are to the speaker, as you approach the speaker you will hear a more intense sound level (given a near field environment).
-    Sound will be absorbed and reflected when it comes into contact with a barrier.  The degree of absorption and reflection has to do with the material the sound comes into contact with.
-    Lower frequencies of sound need a larger barrier to reflect them due to their longer wavelength.
-    When sound gets reflected inside a room, waveforms can sum or cancel to create areas of higher or lower intensity.
-    Reflections can also cancel out sound of particular frequencies (comb filtering) or create areas of constant pressure (standing waves).

These factors (and others) determine the quality and loudness of how a sound source will be perceived in a room and they help explain how a speaker cab may sound louder/more bass heavy/worse in one room than another.  Sound pressure levels are very sensitive to environmental factors.  This is important to note because later we will use math to calculate a special case dealing with sound pressure (called coherent summing).

http://www.usmotors.com/TechDocs/ProFacts/Sound-Po wer-Pressure.aspx

With this background information, we are ready to tackle the main issue.  Here is a link to part 2:

http://profile.ultimate-guitar.com/gumbilicious/bl og/110903/
3:45 am - 1 comments - 0 Kudos - Report!
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311ZOSOVHJH wrote on Oct 23rd, 2012 11:55pm

really good stuff man

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