# More acoustic beamformer questions

Started by October 26, 2003
```I was just wondering if an acoustic beamformer can be made to work in
reverse. Suppose we have say eight loud speakers, can the sound be
focused in a narrow 'corridor'? To a certain extent I expect hi-fi
surround sound is doing something similar but there the speakers
surround you - here they would be together in an array.I wonder What
would happen in the limit ifwe could have say 100 small loud speakers or
similar transducers?

Tom

```
```Yes, the equations work both ways.  With speakers, don't forget that you need
to recognize the pattern multiplication rule in your calculations.

In article <3F9C3087.C9EC374C@nOpam.com>, Tom <somebody@nOpam.com> wrote:
>I was just wondering if an acoustic beamformer can be made to work in
>reverse. Suppose we have say eight loud speakers, can the sound be
>focused in a narrow 'corridor'? To a certain extent I expect hi-fi
>surround sound is doing something similar but there the speakers
>surround you - here they would be together in an array.I wonder What
>would happen in the limit ifwe could have say 100 small loud speakers or
>similar transducers?
>
>Tom
>
>
```
```Tom <somebody@nOpam.com> wrote in message news:<3F9C3087.C9EC374C@nOpam.com>...
> I was just wondering if an acoustic beamformer can be made to work in
> reverse. Suppose we have say eight loud speakers, can the sound be
> focused in a narrow 'corridor'? To a certain extent I expect hi-fi
> surround sound is doing something similar but there the speakers
> surround you - here they would be together in an array.I wonder What
> would happen in the limit ifwe could have say 100 small loud speakers or
> similar transducers?

If you let only the maths work in an ideal world, you would be able to
make a "phased array" speaker system that could steer the sound to
go in different directions or otherwise manipulate the sound.

In the case of audio, I believe you would encounter a couple of
practical difficulties with speaker element sizes and acoustic
wavelengths.

Sound travels through air at 330 m/s. The wavelength lambda depends on
frequency as:

f =   1000 Hz  -  lambda = 33   cm
f =  10000 Hz  -  lambda =  3   cm
f =  20000 Hz  -  lambda =  1.5 cm

So the wavelengths are roughly on the same scale as the physical speaker
elements you need to produce the sound. Which in itself introduces some
difficulties, first of all because beamformers need to control the positions
of the elements to within fractions of a wavelength, second because, as
others have mentioned, you need to account for the directivity of individual
speaker elements, which becomes more difficult the larger the speaker
element is (in terms of wavelengths).

Again, these objections are due to practical restrictions of audio
equipment. Your basic idea is correct, beamformers can be used for either
analysis of measured signals or synthesis/production of projected signals.

Rune
```
```allnor@tele.ntnu.no (Rune Allnor) wrote in message news:<f56893ae.0310262311.45922740@posting.google.com>...
>
> Sound travels through air at 330 m/s. The wavelength lambda depends on
> frequency as:
>
> f =   1000 Hz  -  lambda = 33   cm
> f =  10000 Hz  -  lambda =  3   cm
> f =  20000 Hz  -  lambda =  1.5 cm
>
> So the wavelengths are roughly on the same scale as the physical speaker
> elements you need to produce the sound. Which in itself introduces some
> difficulties, first of all because beamformers need to control the positions
> of the elements to within fractions of a wavelength, second because, as
> others have mentioned, you need to account for the directivity of individual
> speaker elements, which becomes more difficult the larger the speaker
> element is (in terms of wavelengths).
>
> Again, these objections are due to practical restrictions of audio
> equipment. Your basic idea is correct, beamformers can be used for either
> analysis of measured signals or synthesis/production of projected signals.
>
> Rune

I am unsure what you mean by the 'speaker elements' - do you mean the
diameter of the speaker cone for instance? Are you suggesting that the
smaller speaker the better? ie if the speaker diameter is d then
lambda <<d say <0.1d where lambda is the speaker diameters so
realistically it could only work for low frequencies with preent
technology?

Thanks

Tom
```
```"Tom" <somebody@nOpam.com> wrote in message
news:3F9C3087.C9EC374C@nOpam.com...
> I was just wondering if an acoustic beamformer can be made to work in
> reverse. Suppose we have say eight loud speakers, can the sound be
> focused in a narrow 'corridor'? To a certain extent I expect hi-fi
> surround sound is doing something similar but there the speakers
> surround you - here they would be together in an array.I wonder What
> would happen in the limit ifwe could have say 100 small loud speakers or
> similar transducers?

Tom,

Rune's post gives you a lot of good information.  Here's more:

Assuming the speakers are all the same and are all driven equally with no
delay elements:

If the speakers are omnidirectional, then you can use relatively simple math
(actually the Fourier Transform) to compute the beam pattern.  This will be
the case for the speakers being small relative to a wavelength.  If the
speakers are larger, then their individual patterns won't be
ominidirectional.

Now, if the speakers aren't omnidirectional these things are modified by the
individual speaker patterns.

If the spacing is very, very small then the end result will be close to a
single speaker's pattern.
The larger the array of speakers, the narrower the beam can be.  So, if your
100 speakers are arranged so that they're 1/10th of a wavelength apart and
cover 10 wavelengths .....
The beamwidth of a 1/2 wavelength spaced linear array is around
51*wavelength/(length of the line) in degrees.  So 100 elements would
suggest a beamwidth of 51/50= 1 degree.

Fred

```
```It is nearly impossible to get omni-directional speakers in air.  It is much
easier in water where the sound speed is higher (1500 m/s vice 335 m/s) and
the impedance makes it easier to load the source.  Generally the bandwidths
are smaller,  Qs are typically 4 to 6, and a quarter wavelength source is a
reasonable size (half the size of a Volkswagen and a few tons) and is only an
eigth of a dB or so from omni for 230 dB SPL.

<fmarshallx@remove_the_x.acm.org> wrote:
>
>"Tom" <somebody@nOpam.com> wrote in message
>news:3F9C3087.C9EC374C@nOpam.com...
>> I was just wondering if an acoustic beamformer can be made to work in
>> reverse. Suppose we have say eight loud speakers, can the sound be
>> focused in a narrow 'corridor'? To a certain extent I expect hi-fi
>> surround sound is doing something similar but there the speakers
>> surround you - here they would be together in an array.I wonder What
>> would happen in the limit ifwe could have say 100 small loud speakers or
>> similar transducers?
>
>Tom,
>
>Rune's post gives you a lot of good information.  Here's more:
>
>Assuming the speakers are all the same and are all driven equally with no
>delay elements:
>
>If the speakers are omnidirectional, then you can use relatively simple math
>(actually the Fourier Transform) to compute the beam pattern.  This will be
>the case for the speakers being small relative to a wavelength.  If the
>speakers are larger, then their individual patterns won't be
>ominidirectional.
>
>Now, if the speakers aren't omnidirectional these things are modified by the
>individual speaker patterns.
>
>If the spacing is very, very small then the end result will be close to a
>single speaker's pattern.
>The larger the array of speakers, the narrower the beam can be.  So, if your
>100 speakers are arranged so that they're 1/10th of a wavelength apart and
>cover 10 wavelengths .....
>The beamwidth of a 1/2 wavelength spaced linear array is around
>51*wavelength/(length of the line) in degrees.  So 100 elements would
>suggest a beamwidth of 51/50= 1 degree.
>
>Fred
>
>
>
```
```aberdonian_2000@yahoo.com (Tom) wrote in message news:<e1b1658f.0310271224.532cd447@posting.google.com>...
> allnor@tele.ntnu.no (Rune Allnor) wrote in message news:<f56893ae.0310262311.45922740@posting.google.com>...
> >
> > Sound travels through air at 330 m/s. The wavelength lambda depends on
> > frequency as:
> >
> > f =   1000 Hz  -  lambda = 33   cm
> > f =  10000 Hz  -  lambda =  3   cm
> > f =  20000 Hz  -  lambda =  1.5 cm
> >
> > So the wavelengths are roughly on the same scale as the physical speaker
> > elements you need to produce the sound. Which in itself introduces some
> > difficulties, first of all because beamformers need to control the positions
> > of the elements to within fractions of a wavelength, second because, as
> > others have mentioned, you need to account for the directivity of individual
> > speaker elements, which becomes more difficult the larger the speaker
> > element is (in terms of wavelengths).
> >
> > Again, these objections are due to practical restrictions of audio
> > equipment. Your basic idea is correct, beamformers can be used for either
> > analysis of measured signals or synthesis/production of projected signals.
> >
> > Rune
>
> I am unsure what you mean by the 'speaker elements' - do you mean the
> diameter of the speaker cone for instance?

That's what I mean.

> Are you suggesting that the
> smaller speaker the better? ie if the speaker diameter is d then
> lambda <<d say <0.1d where lambda is the speaker diameters so
> realistically it could only work for low frequencies with preent
> technology?

Well, yes. All beamformers I know of (which, by the way, are sensors,
not projectors) rely on the individual elements being small in terms
of wavelength. It solves the spacing problem and for sufficiently small
sizes, the elements can be regarded as isotropic monopoles, i.e. the
individual sensor directivity patterns can be neglected.

Rune
```
```<nobody@nowhere.nothing> wrote in message
news:pzhnb.71908\$th6.65656@twister.socal.rr.com...
> It is nearly impossible to get omni-directional speakers in air.  It is
much
> easier in water where the sound speed is higher (1500 m/s vice 335 m/s)
and
> the impedance makes it easier to load the source.  Generally the
bandwidths
> are smaller,  Qs are typically 4 to 6, and a quarter wavelength source is
a
> reasonable size (half the size of a Volkswagen and a few tons) and is only
an
> eigth of a dB or so from omni for 230 dB SPL.

And here I thought a "boom box" in a Volkswagen was omni!
[thump, thump, thump......]

```
```Hi Tom, Rune and Fred

I noticed one thing missing.  A common mistake when summing the signals
is that you cant sum power.  Instead you need to sum voltage, or in this
case its equivilent (if I remember correctly this is atmospheric pressure).

Consider the power density at a given radius R from the center

P_R = Pin/R^2

Therefor for Voltage, that you can sum, you need to take the square root

V_R = V_in/R

I ran into this many years ago when I designed a 'line source' array of
for a moment you can visualize that at a given finite distance you will
be closer to some speakers than others and that the resulting wavefront
will not be spherical (like with one speaker) but a limited length
(truncated) cylinder.

Solving for the frequency response for any arbitrary point is an
interesting problem.  I did so using calculus (difficult), FFT of the
imulse response and a direct computer simulation.  All three matched,
but what was interesting was that it gave a 3db/octave rolloff of the
high frequencies.  Better yet... it matched the measured response.

After taking the rolloff into account, these speakers sounded great.
But what was more interesting was that the stereo imaging was improved,
and without having to sit in a 'sweet spot' like you do with small
speakers with 1 driver.

+------------------------------------------+
|Keith Larson                              |
|Member Group Technical Staff              |
|Texas Instruments Incorporated            |
|                                          |
| 281-274-3288                             |
| k-larson2@ti.com                         |
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+------------------------------------------+

```
```Keith Larson wrote:

> Hi Tom, Rune and Fred
>
> I noticed one thing missing.  A common mistake when summing the signals
> is that you cant sum power.  Instead you need to sum voltage, or in this
> case its equivilent (if I remember correctly this is atmospheric pressure).
>
...

Pressure or velocity interchangeably in the far field. The near field
velocity is frequency sensitive. That's why ribbon microphones, which
are velocity sensitive, provide bass boost for close talking.

Jerry
--
Engineering is the art of making what you want from things you can get.
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```