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<p class="ArticleTitle"><font size="5">The Doppler Effect<br>
</font><font color="#000000" size="4"><strong>Lesson 7</strong></font></p>
<p align="right" class="ArticleAuthor">Author: <a href="mailto:lightonthewater@hotmail.com">Jesse
Maurais</a><br>
Adapted For Java By: <a href="mailto:athomas@dev.java.net">Athomas Goldberg</a></p>
<h1>A Look at Real-World Physics</h1>
<p align="justify">I know this will be boring review for anyone with a course
in high school physics, but lets humour ourselves. The Doppler effect can be
a very tricky concept for some people, but it is a logical process, and kind
of interesting when you get right down to it. To begin understanding the Doppler
effect we first must start to understand what a "sound" really is.
Basically a sound is your minds interpretation of a compression wave that is
traveling through the air. Whenever the air becomes disturbed it starts a wave
which compresses the air particles around it. This wave travels outward from
it's point of origin. Consider the following diagram.</p>
<p align="justify"><img src="sound_waves.jpg" width="150" height="132" hspace="5" vspace="0" border="0" align="left">In
this diagram (on the left) the big red "S" stands for the sources
position, and the big red "L" stands for (you guessed it), the Listener's
position. Both source and Listener are not moving. The source is emitting compression
waves outward, which are represented in this diagram by the blue circles. The
Listener is experiencing the sound exactly as it is being made in this diagram.
The Doppler effect is not actually present in this example since there is no
motion; the Doppler effect only describes the warping of sound due to motion.</p>
<p align="justify">What you should try to do is picture this diagram animated.
When the source emits a wave (the circles) it will look as though it is growing
away from it's point of origin, which is the sources position. A good example
of a similar effect is the ripples in a pond. When you throw a pebble into a
calm body of water it will emit waves which constantly move away from the point
of impact. Believe it or not this occurs from the exact same physical properties.
But what does this have to do with the Doppler effect? Check out the next diagram
(on the right).</p>
<p align="justify"> <img src="doppler_effect.jpg" width="150" height="132" hspace="5" border="0" align="right">Wow,
what's going on here? The source is now in motion, indicated by the little red
arrow. In fact the source is now moving towards the Listener with an implied
velocity. Notice particularly that the waves (circles) are being displaced inside
each other. The displacement follows the approximate path of the source which
emits them. This is the key to the Doppler effect. Essentially what has happened
is that the source has emitted a wave at different points in it's path of travel.
The waves it emits do not move with it, but continue on their own path of travel
from the point they were emitted.</p>
<p align="justify">So how does this effect the perceived sound by the Listener?
Well, notice too in the last diagram that the waves (circles) that are between
the source and the Listener are kind of compressed together. This will cause
the sound waves to run together, which in turn causes the perceived sound seem
like it's faster. What we are talking about here is frequency. The distances
between the waves effects the frequency of the sound. When the source that emits
the sound is in motion, it causes a change in frequency. You may notice too
that distance between the waves varies at different points in space. For example,
on the opposite side of the moving source (anywhere along the previous path
of travel) the distances are actually wider, so the frequency will be lower
(the distance and frequency have an inverse relationship). What this implies
is that the frequency perceived by the Listener is relative to where the Listener
is standing. </p>
<p align="justify">The motion of the Listener can also affect the frequency. This
one is a little harder to picture though. If the source is still, and the Listener
is moving toward the source, then the perceived frequency by the Listener will
be warped in the same exact manner that we described for the moving source.
</p>
<p>If you still have trouble picturing this, consider the following two
diagrams:</p>
<p align="center"><img border="0" src="sin_wave.jpg" width="255" height="135">
<img border="0" src="compress_sin_wave.jpg" width="255" height="135"></p>
<p align="justify">These two diagrams will represent the sound in the form of
a sine wave. Look at the first one. Think of the peaks as the instance of the
wave. The very top point of the wave will be the same as the instance of the
blue circle in the previous set of diagrams. The valleys will be like the spaces
in between the blue circles. The second diagram represents a compressed wave.
When you compare the two you will notice an obvious difference. The second diagram
simply has more wave occurrences in the same amount of space. Other ways of
saying this are that they occur more often, with a greater regularity, or with
a greater frequency. </p>
<p align="justify">For anyone who is interested in some added information: The
velocity of the waves is the speed of sound. If the velocity of the source is
greater than that of the wave, then the source is breaking the sound barrier.</p>
<h1>The Physics of OpenAL</h1>
<p align="justify">Ok, either you have understood my ramblings on the Doppler
effect from above, or you have skipped it because you already have full knowledge
of the Doppler effect and just want to know how it effects the OpenAL rendering
pipeline. I think the best start to his section will be to quote the OpenAL
spec directly:</p>
<blockquote>
<p align="justify"><i>"The Doppler Effect depends on the velocities of
Source and Listener relative to the medium, and the propagation speed of sound
in that medium." - chapter 3, subsection 7"</i></p>
</blockquote>
<p align="justify">We can take this to mean that there are 3 factors which are
going to affect the final frequency of the sound heard by the Listener. These
factors are the velocity of the source, the velocity of the Listener, and a
predefined speed of sound. </p>
<p align="justify">When we refer to a "medium", what we mean is the
kind of material that both the source and Listener are "in". For example,
sounds that are heard from underwater are much different than sounds that are
heard in the open air. Air and water are examples of different mediums. The
reason that sound is so different between these mediums has to do with the particle
density. As we said before, sound is nothing but the motion of particles in
the air. In a medium with a much greater particle density the sound will be
much different because the particles are in closer contact. When they are in
closer contact it allows for the wave to travel much better. As an example of
the opposite, think of outer space. In outer space there is an extremely low
particle density. In fact there is only a few very light particles (mostly hydrogen)
scattered about. This is why no sound can be heard from space. </p>
<p align="justify">Ok, lets get back on topic. OpenAL calculates the Doppler effect
internally for us, so we need only define a few parameters that will effect
the calculation. We would do this in case we don't want a realistic rendering.
Rather if want to exaggerate or deemphasize the effect. The calculation goes
like this.</p>
<p><span class="codeNormal"> shift = DOPPLER_FACTOR * freq * (DOPPLER_VELOCITY
- l.velocity) / (DOPPLER_VELOCITY + s.velocity)</span></p>
<p align="justify">Constants are written in all caps to differentiate. The "l"
and "s" variables are the Listener and source respectively. "freq"
is the initial unaltered frequency of the emitting wave, and "shift"
is the altered frequency of the wave. The term "shift" is the proper
way to address the altered frequency and will be used from now on. This final
shifted frequency will be sampled by OpenAL for all audio streaming that is
affected. </p>
<p align="justify">We already know that we can define the velocity of both source
and Listener by using the 'AL_VELOCITY' field to 'alListenerfv' and 'alSourcefv'.
The 'freq' parameter comes straight from the buffer properties when it was loaded
from file. To set the constant values the following functions are provided for
us.</p>
<pre class=code><font color="#0000FF">public void </font>alDopplerFactor(<font color="#0000FF">float</font> factor);
<font color="#0000FF">public void </font>alDopplerVelocity(<font color="#0000FF">float</font> velocity);
</pre>
<p align="justify">For 'alDopplerFactor' any non-negative value will suffice.
Passing a negative value will raise an error of 'AL_INVALID_VALUE', and the
whole command will be ignored. Passing zero is a perfectly valid argument. Doing
this will disable the Doppler effect and may in fact help overall performance
(but won't be as realistic). The effect of the Doppler factor will directly
change the magnitude of the equation. A value of 1.0 will not change the effect
at all. Passing anything between 0.0 and 1.0 will minimize the Doppler effect,
and anything greater than 1.0 will maximize the effect. </p>
<p align="justify">For 'alDopplerVelocity' any non-negative non-zero value will
suffice. Passing either a negative or a zero will raise an error of 'AL_INVALID_VALUE',
and the whole command will be ignored. The Doppler velocity is essentially the
speed of sound. Setting this will be like setting how fast sound can move through
the medium. OpenAL has no sense of medium, but setting the velocity will give
the effect of a medium. OpenAL also has no sense of units (kilometer, miles,
parsecs), so keep that in mind when you set this value so it is consistent with
all other notions of units that you have defined.</p>
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