Mechanical wave diffraction

[thadman]

Excuse me if this question is obvious.

Do mechanical waves propagate through loudspeaker diaphragms (whether they be elastic or rigid) in the same way that acoustic waves propagate through waveguides? As far as I understand, reflections occur at the boundaries of the diaphragm due to an impedance mismatch in the same way reflections occur at the mouth of a waveguide.

Could diaphragm geometry be conceived in such a way to optimize its mechanical diffraction / reflection pattern to minimize and distribute the energy over a wider bandwidth?

Thanks,
Thadman

[thadman]

Assuming this is true, where would the source of the mechanical wave occur in a driver where the motor force is distributed uniformly over its surface and for a driver whose motor force is not distributed uniformly?

[CLS]

I think of the Quad. They claimed the center region got larger driving force thus slightly bigger amplitude then the surrounding. So the wavefront is more spherical than planar.

Correct me if I'm wrong.

I'm wondering how this can be done within an ordinary cone/dome driver. Maybe some kind of coaxial with a relatively large center portion? But how to use such a monster?

[thadman]

Originally posted by CLS
I think of the Quad. They claimed the center region got larger driving force thus slightly bigger amplitude then the surrounding. So the wavefront is more spherical than planar.

Correct me if I'm wrong.

I'm wondering how this can be done within an ordinary cone/dome driver. Maybe some kind of coaxial with a relatively large center portion? But how to use such a monster?

A higher displacement at the center may not necessarily be due to a larger driving force in the center. It will exhibit the same behavior due to a higher torque at the center with a uniform force distribution. Regardless, in such a circumstance, where would the source of the mechanical wave be?

[bear]

May not be what you are thinking of... look into the design concept behind the Manger driver.

_-_-bear

[rcw]

The subject of cones was researched in the 70,s by Philips and such people as KEF and various BBC workers.
The model used was generally that of an aperiodic transmission line, and it was found that a hyperbolic cone shape smoothly decouples as frequency goes up, this minimising the surround reflections.
B&W for instance say that their Kevlar cones further reduce surround reflection effects because the woven structure results in the outgoing and incoming wavefronts being a different shape.
rcw

[bear]

could we define "aperiodic transmission line"?

_-_-bear

[rcw]

Aperiodic just means having no resonaces.
rcw

[thadman]

In acoustics, if we placed a point source at an arbitrary location in a room of arbitrary dimensions, it would pressurize the room uniformly below the room fundamental and excite modal resonances above the fundamental due to reflections at the walls (ie boundaries, the mechanism is due to an impedance mismatch between the air and the walls). However, if we were to place an infinite number of sources in a particular plane, a modal structure could not be supported in that plane and as a result it would be uniformly pressurized. I believe this is the knowledge behind Dr. Geddes' theory of multiple subwoofer arrangements.

How can we relate this acoustic example to a loudspeaker diaphragm?

As far as I understand, when diffraction occurs at a boundary, a new source is created. If we diffract the mechanical wave as it passes through the diaphragm, new sources are created, distributing the sources over the surface of the diaphragm analogous to Dr. Geddes' approach to subwoofer arrangements.

[gedlee]

Originally posted by thadman
Excuse me if this question is obvious.

Do mechanical waves propagate through loudspeaker diaphragms (whether they be elastic or rigid) in the same way that acoustic waves propagate through waveguides? As far as I understand, reflections occur at the boundaries of the diaphragm due to an impedance mismatch in the same way reflections occur at the mouth of a waveguide.

Could diaphragm geometry be conceived in such a way to optimize its mechanical diffraction / reflection pattern to minimize and distribute the energy over a wider bandwidth?

Thanks,
Thadman

I didn't quite see the question answered. Yes mechanical waves do propagate through a loudspeaker cone, but unlike acoustics two types of waves are possible - compressional waves (also called longitudinal) and bending waves (also called transverse). The dominate wave in a cone is transverse, but compressional waves can exists. Reflections do occur at the edge of the cone and the method of cone termination is critical to the performance of the driver just above its piston range.

I think that you mean "reflection" since "diffraction" of the mechanical wave in the diaphragm is not an issue. The "geometry" of the cone (straight, exponential) has a minimal effect, but no shape can have no resonances. In fact it can be shown that all shapes of the same material will have the same lowest resonant frequency that depends only on the area (the shape is irrelavent) The surround and the edge treatment has a major effect however. Usually the most serious cone resonance is the first one where the cones edge begins to "flap". It does this first in phase with the drive, but then as the frequency goes up and the edge reflection gets greater the outside edge of the cone quickly reverses its phase relative to the main body and goes out of phase. This leads to the classic peak and then a dip at the upper edge of the drivers piston range, usually called the "edge hole".

How this critical range is controlled is IMO the key to the driver. Its very tricky to get right and still have a large excusion capability. Not many drivers do get this right and it seriuosly limits there usefulness.

Above this first "mode" the cone is basically out of control no matter what you do and it is resonating all over the place - its pretty much useless at these frequencies. Its either highly resonant or its dead with no sound radiation at all. There aren't really any other options.