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]

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]

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.

 

[thadman]

Re: Re: Mechanical wave diffraction

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.

Thanks for the insight Earl, your comments are enlightening and much appreciated. I couldn't thank you enough for your presence on this forum, your knowledge and research is a huge resource to this DIY community.

The way I understand it, the reason the first mode is independent of dimension is analogous to the subwoofer with multiple ports of varying cross-sectional area and length. The ports sum to one total acoustic mass and cross-sectional area and the system functions as the sum of its constituents for the first mode. However, above the fundamental the multiple ports will have different modal patterns due to their geometry. Is this explanation accurate? If it is incorrect or incomplete, I would much appreciate some feedback.

With regard to resonances, since every driver has edge boundaries, a reflection must occur at these boundaries due to the impedance mismatch. It is unavoidable and as a result there will be interference between the reflections and the primary transverse waves. However, this statement makes no mention of the amplitude of the reflection. In what ways can we minimize these reflections or optimize their interaction with the primary transverse waves other than decreasing the distance between the boundaries (reflections are in-phase with primary waves)? Can we apply any of your knowledge relating to waveguides and acoustic waves to mechanical boundaries and transverse waves?

In most drivers, thickness is a negligible dimension relative to its other dimensions and since compressional (longitudinal) waves are dependent upon thickness (they propagate parallel to the travel direction of the wave energy) they should not be supported. Could this explain the reason why they are usually not considered? In what situations would compressional (longitudinal) waves exist?

In acoustics, diffraction becomes a factor when the wavelength approaches the dimensions of the enclosure. This should explain the baffle-step phenomenon. I believe Linkwitz recommends a radius of 1/4 wavelength for the lowest supported wave to distribute the diffraction sources. How can we relate this knowledge to mechanical waves? Would mechanical diffraction occur if the cone angle approached the dimensions of the mechanical transverse waves?

Is there a distinction between the generation of transverse waves with regards to the distribution of the load (dynamic cone approaches a point load, ribbon/ESL approach a uniform load)? If so, what is the relationship?

Thanks,
Thadman

 

[gedlee]

Re: Re: Re: Mechanical wave diffraction

The way I understand it, the reason the first mode is independent of dimension is analogous to the subwoofer with multiple ports of varying cross-sectional area and length. The ports sum to one total acoustic mass and cross-sectional area and the system functions as the sum of its constituents for the first mode. However, above the fundamental the multiple ports will have different modal patterns due to their geometry. Is this explanation accurate? If it is incorrect or incomplete, I would much appreciate some feedback.

The first mode tends to be independent of shape, it is highly dependent on dimensions. But your analogy is OK, not ideal but good enough. At the first mode the wavelengths are too long to see shape. In the ports the wavelength is too long to see individual ports, it only see one average one.

With regard to resonances, since every driver has edge boundaries, a reflection must occur at these boundaries due to the impedance mismatch. It is unavoidable and as a result there will be interference between the reflections and the primary transverse waves. However, this statement makes no mention of the amplitude of the reflection. In what ways can we minimize these reflections or optimize their interaction with the primary transverse waves other than decreasing the distance between the boundaries (reflections are in-phase with primary waves)? Can we apply any of your knowledge relating to waveguides and acoustic waves to mechanical boundaries and transverse waves?

The reflection is most effectively reduced with a soft multiple role suspension that is well damped and about the same density as the cone. The large very big heavy role suspensions may be good for excusrion but they are terrible at edge termination.


In most drivers, thickness is a negligible dimension relative to its other dimensions and since compressional (longitudinal) waves are dependent upon thickness (they propagate parallel to the travel direction of the wave energy) they should not be supported. Could this explain the reason why they are usually not considered? In what situations would compressional (longitudinal) waves exist? [/B][/QUOTE]
None of any significance

In acoustics, diffraction becomes a factor when the wavelength approaches the dimensions of the enclosure. This should explain the baffle-step phenomenon. I believe Linkwitz recommends a radius of 1/4 wavelength for the lowest supported wave to distribute the diffraction sources. How can we relate this knowledge to mechanical waves? Would mechanical diffraction occur if the cone angle approached the dimensions of the mechanical transverse waves?

Is there a distinction between the generation of transverse waves with regards to the distribution of the load (dynamic cone approaches a point load, ribbon/ESL approach a uniform load)? If so, what is the relationship?

Thanks,
Thadman

Diffraction is the bending of waves arround an obstacle. It takes some disatnce relative to the wavelengths for this to occur and the mechanical transverse waves basically don't have enough space.

The last question is extremely complex and each situation is different. There really arn't any generalizations that one can make.

 

[rcw]

An interesting paper about cone materials and the first bending mode is here….

http://www.infinitysystems.com/home...apers.aspx?Language=ENG&Country=US&Region=USA

The methods pioneered in the 70,s by the British makers was to use damped low velocity materials like Bextrene and later Polypropylene to extend the useful frequency range well up above the piston range.
This resulted in the small two way "BBC" type systems by such as Spendor and Rogers, these were greatly admired by many people as having very natural and un coloured sound, and the technique of using heavily damped highly curved cones with progressive cone decoupling is still widely used.
These days there is a trend towards pushing up the piston range by the use of stiff light weight materials such as Aluminium and Titanium, an Aluminium cone for instance has a piston range that extends some two octaves higher than that of a Polypropylene one.

The piston range can be said to be the range over which mechanical waves do not travel through the cone but all parts of the cone move in unison in the same way as a piston does. Once the cone actually starts to flex then its shape construction material and termination determine what happens next.
As Earl observed cones are made from elastic solids and can therefore sustain both compressional and shearing forces whereas air being a gas can only sustain compressional waves.
Exactly which of these two approaches is best tends to depend upon how well it is done not upon the method itself.
Rcw.

 

[thadman]

Re: Re: Re: Re: Mechanical wave diffraction

The reflection is most effectively reduced with a soft multiple role suspension that is well damped and about the same density as the cone. The large very big heavy role suspensions may be good for excusrion but they are terrible at edge termination.

What material properties should we consider if we wished to determine the damping coefficient of shear waves in Aluminum and other popular diaphragm materials?

At what point (if ever) does geometry affect a material's damping properties?

 

[thadman]

I'm also curious whether you'd consider the viscous, hysteretic, or fractional (combination of viscous and hysteretic) damping models for small displacements as best describing the behavior of shear waves in Aluminum and other popular diaphragm materials.

Thanks,
Thadman

 

[gedlee]

Hi Thadman

I think that Shear Wave is not a correct phrase. The main vibrational modes in a diaphragm are transverse, which does have some shear, but it mostly bending. A thin membrane cannot bend without some shear, but the shear effect is small.

As to the damping in alluminum, or any metal for that matter, you can consider the damping to be negligable, certainly insignificant. The damping comes from the surround in almost all cases and is viscous usually the result of the soft compound with high internal damping painted on a semi porous material.

 

[soongsc]

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

Some research was done in this area. JVC has a design basically is such that the VC is off center in relation with the cone diaphragm, you could also design a cap to be off center.

 

[gedlee]

Re: Re: Mechanical wave diffraction

Some research was done in this area. JVC has a design basically is such that the VC is off center in relation with the cone diaphragm, you could also design a cap to be off center.

Or you could design the whole system to be random - I have some patent disclosures on that.

 

[soongsc]

And you've build one one that actually works?

 

[gedlee]

And you've build one one that actually works?

No comment at this time.