Transition of Mechanical Waves (Solids to Gases and vice versa)

[elandres]

As a hobby, I have been researching the different aspects of modeling the sounds produced by musical instruments. Particularly, I want to create as accurate a model as possible, and not something very simple (to which many may ask "why?" if complexity will reduce the likeliness of real time implementation, in which case a sampled recording might be preferable anyways -- again its a hobby).

That said, in my review of mechanical and sound waves, I've not found the link between waves in solids (vibrations) and the resulting sound waves propagated by them. Searching online has been difficult, as I am not sure what to search for; I've tried "coupling between solids and gases," "transition of sound between mediums," etc. My instinct tells me that my answer lies in somewhere in between the disciplines of rigid body and fluid mechanics, neither of which I am that strong in.

As a particular example, an acoustic guitar involves a plucked string that produces an initial sound, which is then resonated by an enclosed volume. The string vibration can be modeled as a transverse wave. Yet somehow it excites the air around it to produce the longitudinal sound waves, which are directed in all directions outward and perpendicular to the length of the string (something tells me that this is only partly true as the distortion of the string is assumed to be in one direction). A little more than half of the waves would propagate away from the guitar, without the resonating effects. Another portion would reflect off the guitar itself and then away from the guitar. And the remaining waves will travel into resonating cavity of the guitar, and then propagate outwards. In summation the resulting sound, would be the combination of those waves.

 

[Unrest]

Acoustics involving reflections are notorously hard to model accurately, and can take stupendous amounts of computer time. To the point where they often still use scale models isntead of computers.

The sound from a guitar should be very different when heard from different directions. There might even be different interferences between waves reflected/generated at different parts of the instrument.

You can find resonant frequencies in cavities fairly easily tho. But it's beyond me how you'd work out their amplitudes and phases to know how they'd interfere with the sound generated by the strings.



Here's something from a magazine article:

"A piezoacoustic device model needs three different physics: piezoelectric stress-strain, an electric field, and pressure acoustics in a fluid. Only a multiphysics-capable simulation can define a computer model that couples the involved phenomena. ...
The boundary condition for the acoustics sets the pressure equal to the normal acceleration of the solid domain at the air and crystal interface. This drives the pressure in the air domain. On the other hand, the crystal domain is subjected to the acoustic pressure changes in the air domain."

 

[Studiot]

I am unclear about your actual question.

Are you asking about the transduction process, the influence of materials on the produced sound quality, or...?

 

[AlephZero]

As a particular example, an acoustic guitar involves a plucked string that produces an initial sound, which is then resonated by an enclosed volume. The string vibration can be modeled as a transverse wave. Yet somehow it excites the air around it to produce the longitudinal sound waves, which are directed in all directions outward and perpendicular to the length of the string (something tells me that this is only partly true as the distortion of the string is assumed to be in one direction).

The string does not excite the air directly, to any significant extent.

The vibrating string creates a force on the guitar bridge that makes the body of the guitar vibrate. The vibration of the guitar body in the direction perpendicular to its surface is what makes the air vibrate.

The air inside the guitar also vibrates, and is coupled to the air outside by the sound-hole on the front of the guitar.

Modeliing the physics of this directly is difficult. One reason is because the mechanical behaviour of wood is much more complicated than metal. Another reason is that you have to model the air outside the guitar extending to infinity in all directions, otherwise you are not modelling the sound of the guitar itself, but the guitar played in a particular space.

A more practical approach that is part experimental and part computational is to measure the response of the guitar body. You can do that (in principle) by removing the guitar strings, and tapping the bridge with something, recording the sound produced, and analysing the recording to find the resonant frequences the amount of damping (i.e. how fast each frequency decays, after a short "tap"). You can then model the vibration of the string on its own (which is easy) and create the guitar sound by adding up the effect of each "tap" that the string applies to the guitar body.

To get "good" results with a guitar, you also need to model the effect of the player's fingers pressing the strings against the frets, and/or bending the strings to change the pitch, which is another large complication. There are some pretty good models of pianos that have been created this way, for example http://www.pianoteq.com

For Google buzzwords, try "fluid-solid interaction".