Acoustic horns and impedance matching

[parsec]

I found a fast solenoid valve lying around (~1ms rise time) so I thought it would be fun to hook up to a compressed air line and use to generate some really loud bass. I hooked it up to a function generator and air supply only to find that it was disappointingly quiet (well not quiet, but nowhere near as loud as I was expecting for 80psi of overpressure).

I did some thinking and reading on the topic and realized there is probably some impedance mismatch issue at play, which is a little puzzling. I found an old broken trombone and brazed on a fitting to the horn to connect it to the solenoid valve. It made the setup greatly louder, however most of the energy was in higher order harmonics (still, not much bass was generated).

My impression is that acoustic horns are required to match the impedance for compression drivers because the driver membrane needs to generate a high pressure against significant resistance (high throat impedance). The gas then expands to a greater area and lower peak pressures (and higher velocities).

Why is this also the case for compressed air? An explosion or other kinds of overpressure events generate loud sounds, yet my solenoid valve expanding directly into the atmosphere (sans horn) isn't so loud, especially at low frequencies.

Is the function of the horn in this context to allow the air to expand in one direction, converting the high pressure into high velocity particles moving in one direction? Kind of like a nozzle on a rocket converting the disordered motion of high temperature, high pressure gases into lower pressure and temperature gases moving in one direction (axially, out of the nozzle).

Is the perceived efficiency gain I am getting in my compressed air setup therefore not a result of impedance matching, but simply the result of a collimation and directional expansion of the compressed gas (a kind of second law efficiency gain)?

I would like to know what the transfer function of my horn is (or any horn as a function of frequency) in this context, but I don't really know where to begin. Most of the derivations I have seen yield acoustic impedances, but I don't know how applicable that is here to a fluctuating source of compressed air instead of a reciprocating membrane (speaker/compression driver). Conventional theory suggests that throat impedance needs to be closely matched to driver impedance, but I have no driver in this scenario.

 

[DennisN]

Hi parsec,

I don't know what your "valve loudspeaker" looks like, but I will tell you a couple of things regarding sound reproduction from loudspeakers and acoustic horns:

1. In order to get a proper sound output from a speaker driver, the driver needs to have an enclosure (see http://hyperphysics.phy-astr.gsu.edu/hbase/audio/spk2.html#c1). Maybe your design is already enclosed, I don't know.

2. In order to reproduce bass sounds, the diagphragm/cone (i.e. the moving part of the driver) needs to be big, not small. The larger the area of the diagphragm/cone is, the more bass will be reproduced. Small diagphragms will not reproduce bass sounds well (see http://hyperphysics.phy-astr.gsu.edu/hbase/audio/spk2.html#c4). Also, the diagphragm/cone must be able to move a considerable distance back and forth to produce bass.

3. Horns for bass drivers needs to be large, LARGE, that is LONG and with a WIDE diameter at the output of the horn (it depends on the maximum wavelength (minimum frequency) that the bass driver should reproduce). E.g. for a bass driver with a diameter of 10 cm and with a min. frequency 60 Hz, the minimum horn length is about 1 meter and the minimum horn diameter is about 35 cm (at the output). Small horns will not do the job. Horns can also be folded (see http://hyperphysics.phy-astr.gsu.edu/hbase/audio/spk.html#c6).

For horn design, see e.g. http://www.google.se/#q=acoustic+horns+design

 

[parsec]

It's just a compressed air line which is modulated by a solenoid valve. There is no moving cone or enclosure. I want to create sound by directly modulating compressed air rather than pushing it using a cone.

Thanks for the links.