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Re: [Phys-L] Suggestions for audio speakers



On 03/11/2013 07:20 AM, Forinash III, Kyle wrote:

I will be teaching a physics of sound class in the fall and I would
like to get a good set of speakers/monitors and amp system (has to be
portable). Does anyone have any recommendations? I have a CD that
plays a sine wave starting at about 20Hz and sweeps up to 20,000 Hz
(I ask students to raise their hands when they can't hear it
anymore). I notice the speakers I have don't respond until around 50
Hz - I can't hear anything above about 10k Hz myself so I don't know
if the speakers I have go to 20 kHz or not.

There are many possible answers, depending on details of the
situation:

1a) For a typical classroom situation, you do not need to pay
for high quality "audiophile" or "studio monitor" equipment.

Reason: The non-idealities of the room will swamp the non-
idealities of the speakers, unless the speakers are really
bad.

1b) OTOH if you really do have a professional audio studio,
then it would make sense to get studio-quality equipment.


2) These days it is easy to get ridiculously good audio
amplifiers. There's some bad stuff out there, including
lots of Radio Shack stuff ... but still, the good stuff
is cheap and plentiful.


3) Physics-lab requirements are sometimes more demanding
than run-of-the-mill audiophile requirements.

For example, suppose you want to put out a brief sharp
click. This might involve a brief /peak/ voltage of
50 volts into an 8 ohm speaker. This does not require
the speaker to be able to handle 300 watts RMS, because
the duty cycle is essentially zero. A 3 watt speaker
would work fine. It does however require that the
amplifier put out 50 volts without clipping. So ....
if there is any chance you will want to do things like
this, you want the amplifier to be eeeeenormously overbuilt
relative to the speaker.

This is an argument against ordinary powered speakers,
which would otherwise be an excellent suggestion.


4) As a related point, speaker manufacturers tend to spec
the frequency response. However, there is more to the
story. For many physics applications, you care about the
impulse response. This is significant, because it is easy
for the speaker mfgr to keep the frequency response nice
and flat despite screwing up the phase and thereby screwing
up the impulse response.

Let's be clear: The cochlea and the auditory cortex may
look like they are doing a frequency analysis, but in fact
they are doing a lot more than that. For obvious evolutionary
reason, the auditory system is acutely sensitive to what is
going on in the time domain. If a tiger snaps a twig "over
there" you'd like to know about it. You'd like to be able
to localize the sound. See also item (6).

There are some things you can figure out from a power
spectrum, and some things you can't.


5) Suggestion: Start by getting a decent reference /microphone/.
You're going to want one anyway. It's easier to get a
calibrated microphone than a calibrated speaker ... and
then you can use the mike to help evaluate speakers. See
also next item.


6) This may be more information than you ever wanted, but
it's a fun story, and it might be useful to somebody some
day:

Note that whales do lots of echolocation. Eyes don't
work too well deep down in the ocean. Good spatial
resolution would seem to require a short, sharp click.
OTOH because of the issues hinted at in item (3) above,
it is hard to emit a delta function. The whales however
are smart. Imagine running a delta function through a
filter that smears the click out over time, so that
it becomes more of a thunk than a click. Transmit that.
When the echo comes back, run it through the inverse
filter! For a linear system, that gives you every bit
as much time/space resolution ... with orders of magnitude
less peak amplitude.

On various occasions, I've done a similar thing.

Remember that a filter is basically a convolution and
that convolution in the time domain is a multiplication
in the frequency domain. Fourier transforms and all that.

Start with an abstract delta function, as a function of
time. Transform to frequency domain. The result is
flat as a function of frequency, with some very specific
phase relationships. At each frequency, multiply by a
chosen function that is a unimodular complex number with
a random phase, independently randomly chosen at each
frequency. Remember this function. It randomizes the
phases. Transform back to real time domain. What you
have is not a delta function, but rather a bunch of
PSEUDO-random noise. It's "pseudo" because you remember
the function; you use the same function every time.

Play this noise through a speaker. Record the results
using a good reference microphone. Fourier transform
the results, and divide out the pseudo-randomization.
You don't need to worry about dividing by zero, because
the numbers are unimodular by construction. Transform
back to real time domain.

Ideally, the recording at this point should be a delta
function. However, in reality it will be an echogram
of the room you are in. It will look like a ginormous
mess.

If you are lucky, early in the waveform you will see a
pulse that corresponds to the time-of-flight from the
speaker to the microphone. This will be followed by
lots of echoes from other stuff.

The point is simple: If that first pulse is smeared
out, it indicates something is wrong with the speaker,
microphone, and/or electronics.

Note: At no point have we done anything that would
overstress an amplifier, speaker, or microphone.

This sounds like a lot of work, but it's not really.
It's just a bunch of standard techniques strung together.
The hard part was coming up with the concept. The
same idea is used for radar, but it's easier for sound,
because you can do it all in software.

7) Keep in mind that point-to-point propagation in 3D
involves /spherical/ wavefronts. Such propagation is
dispersive ... even though plane waves in the same
medium are non-dispersive.

To say the same thing another way: Your speakers are
not going to put out ideal plane waves. Really not.
At some point you may have to take this into account.