Re: [Phys-L] Suggestions for audio speakers

["John Clement" <clement@hal-pc.org>]

Nobody seems to have addressed what you are asking for, so here is an
attempt to do this.
1.  It is impossible to have speakers that have flat response down to 20Hz
that are also portable.  Basically you need large woofers to reproduce low
frequency sounds.  Below the resonance frequency of the cabinet/woofer
system the sound cuts off sharply.  Ported speakers extend the low
frequency, but then the cut off is even sharper.  It is possible to extend
the bass even more with equaliztion, but then the power requirements become
enormous and the excursion of the speakers becomes too large.  A back of the
envelope calculation shows that the wavelength at 20Hz is around
340m/s/20Hz=17m.  One formula for a horn loaded speaker is that
lambda=sqrt(4 pi area) so you need a woofer or horn mouth around 4m across
to maintain high efficiency down to 20Hz.  So in the low frequency end there
is no substitute for size and weight.  Of course this calculation is the
extreme   You can gains some extension in the bass by putting speakers in
the corner of a room.  But if the speakers are designed for flat wall
placement, you will have uneven response.

2.  JD pointed out that room acoustics have a large effect on the sound, and
that is true expecially for the low end, but not so much at the high end.
The big problem at the high end would be the dispersion of the tweeters,
which is narrow at higher frequencies.  Small monitor speakers do exist and
are designed to be close to the listener, aimed directly at them.  So the
students directly in front will hear the high frequency sounds, but those
off axis will not, assuming their high end hearing has not already been
destroyed by loud music.  Good speakers for use in theaters will have
controlled dispersion which is wide enough to cover the audience, but not so
wide as to present mainly reflections.  And of course at short wavelengths 2
speakers will have noticeable nodes and nulls.  Column speakers are designed
to have wide horizontal dispersion, with narrow vertical so as to beam the
sound to the audience without large echoes off the ceiling.

3. Sharp clicks require phase coherence, and most speakers do not have that
because the ear is fairly insensative to this.  The only speaker that I know
of that advertised it could reproduce square waves was the Ohm wave guide
series, and they showed photos to prove it.  But they are very large.

4. Then response down to 20Hz mainly can be felt rather than heard.  Most
instruments do not go below 50Hz with the obvious exception of large organs
which go down to around 32Hz.

5.  There is no specific power requirement for what you need.  It depends on
the room size and the efficiency of the speakers.  Powered speakers are
generally designed for small rooms, but our dance group purchased a pair of
modest sized powered monitor speakers that can fill a fair sized room, but
not at rock concert volume.  In the old days large theaters had huge truck
sized horn loaded speakers that could fill the space with just a few watts
of power and achieve good bass response.  There is an inverse relationship
between the speaker size and the needed power for bass response.

So in the end the best way to purchase speakers is to arrange for a trial in
the intended room.  Good retailers will often allow you to buy them and then
return them if not satisfactory.  Use a decent mike and only 1 speaker
operating to measure the response.  The dispersion curves need to be looked
at as well as the frequency response.  If you really want to get good bass
response the speaker should be against a wall, and not on the traditional
lab table.

Your question did not address what you wanted the students to notice.  Do
you want them to notice interference, or the cut off in their hearing?  Some
young people can hear above 20kHz.  I had a friend who could hear the
ultrasonic "silent" alarms in stores.  He now has a hearing aid.  In my
younger days I could hear the 15kHz whistle that TVs would emit.  Modern LCD
screens do not do this, but some video recordings have this whistle embedded
in them.  The TV audio response was limited to 15KHz when they switched to
stereo because as I recall twice the 15KHz flyback frequency was used to
multiplex the audio.  FM is limited to 19kHz, but in practice usually only
up to 15Khz is transmitted.  Lots of people compress their music severly to
5kHz limits and never notice the difference.  Indeed now many people prefer
the MP3 distorted sound to full frequency undistorted sound.

John M. Clement
Houston, TX

> 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.