Trying to understand acoustic dispersion

[messier88]

Ok, so this needs a bit of explaining. I'm a very amateur scientist... well actually I'm really a sound designer, that is amongst other things I create sound effects. I'm also naturally quite curious and like to ask the question why? as I'm sure do you.

 

So my interest in this topic stems from some sound effects, namely the very famous star wars laser sound created by Ben Burtt which was a recording of himself hammering a steel guy wire. As I understand it the phenomenon of acoustic dispersion is responsible for the high frequencies in the sound moving faster than the low frequencies. Other examples of this sound are this great recording under ice sheets:

 

http://silentlistening.wordpress.com/2008/05/09/dispersion-of-sound-waves-in-ice-sheets/

 

So I'm wondering why this happens in some materials and not others, and really why it happens at all. As I mentioned, I'm not a scientist so layman's terms would be appreciated!

 

Many thanks,

 

Mark

[swansont]

I think it's a matter of there being a resonance. Whatever material you have is going to have certain mechanical characteristics (e.g. stiffness) that tell you how it responds to a shock of some sort, and may have a resonance frequency where it will vibrate. Frequencies at or near the resonance will propagate, while the others will get damped out — the material simply doesn't respond well if you try and make it vibrate at a frequency it doesn't "want" to vibrate at.

[messier88]

Well that makes some sense. I guess it's something to do with the properties of solids that allow this to happen, and I think that ice and metal (from the examples I gave) have similar resonant frequencies. What has me confused is this thing of some frequencies seeming to travel faster than others... is this just an illusion? One of the factors in both of the examples is that the sound has travelled a distance, so is it that if a solid receives an impact the energy propagates around impact and travels further at it's resonant frequency. When received over a distance the effect is multiplied enough that those frequencies arrive first and in the case of something like metal they are the higher ones?

Edited September 24, 2012 by messier88

[swansont]

It's not an illusion; there are dispersive materials. Similar to the idea of resonance, the materials will respond differently to different frequencies. The same reason that the speed is faster in stiffer materials, or varies in gases at different pressures.

[messier88]

I see. That's not exactly what I was expecting. Does anyone know of any sources for this sort of data on different materials? I'd love to see some frequency/speed graphs. How about this idea of waves travelling along an object reaching the end and bouncing back? I'm imagining this happens as the energy has nowhere to dissipate.

 

Thanks so much for your replies so far.

[Enthalpy]

Dispersion comes here because these are flexural waves.

Their equation is like d²u/dt² = d⁴u/dx⁴ (with modulus, density and shape adding proportionality factors) (and add a y direction as needed)

which, if writing the solution as cos(w*t)*cos(k*x) gives a dispersion relation like w² = k⁴.

 

Because waves leave quick propagation media for slower ones, a plate couples sound into air or water better at higher frequency, which implies that high frequencies, which make the attack of a sound brilliant, disappear earlier.

 

On a string instrument, the string better withstands a tension such that sound is faster in it than in air so you get a nice sound from enduring coupling into air. If not, it makes just ptiong at the beginning, from frequencies high enough that the bending stiffness accelerates them. But getting 340m/s from a tight string needs a high tenacity that few materials achieve. Some alloys do, nylon more or less, catgut certainly - and then you need a good elongation, which only catgut offers; it needs low losses as well. It looks surprising, but in 2012 we have no synthetic material better than catgut... Not just from prejudices, but resulting from very physical reasons, which one also hears very distinctly.

[Enthalpy]

A better reason to hear the higher frequencies first is that the microphone is far from the the wide-spectrum crack but near to the ice shelf.

Not coupling from the shelf to water, but just propagation in the shelf, lets higher frequency arrive first at the microphone.

Still a consequence of flexural waves propagating faster at higher frequency.

[Ronald Hyde]

A major factor here ( someone may have already explained this, I haven't read the whole post ) is that sound in solids is carried in two ways

P-waves, pressure or compression, and S-waves, shear or transverse. The P-waves travel faster, if the waves 'go around a corner' or encounter

an obstacle they can be converted from one form to the other. I live in earthquake country, you can actually get a pretty good idea of how

far away a quake was by the difference in arrival time of the two waves.

[Enthalpy]

...sound in solids is carried in two ways

P-waves, pressure or compression, and S-waves, shear or transverse.

Pity, flexural waves are neither compression nor shear.

[Ronald Hyde]

Pity, flexural waves are neither compression nor shear.

 

Well, the P and S waves are propagating in an 'infinite' medium, so the F waves must be propagating an a finite medium, is this guess correct?

For instance the spring in an artificial 'echo chamber' of the type that guitar players use.