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.
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:
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
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.
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.
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.
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).
