Resonance

[scotta740]

Would anyone know where to find a chart or graph of how well materials resonate sound? (Preferably metal,plastic, and wood.) Thanks!

[Craig_Bridge]

Unfortunately, resonance is not simply a property of materials. Shape and dimensions will change the resonance properties of a structure significantly. For example, when a violin or acustic guitar is being manufactured, their resonance properties are checked and tuned by scraping wood to thin the top until the correct frequency resonance is obtained.

All structures will have resonant frequencies no matter what they are made from. The resonant frequences may not be in the audio range.

[scotta740]

I'm gonna go out on a limb here. Are there any equations to determine the resonance if you know the dimensions of the material being used? For example, a block of wood with a length and width of 12cm., and a depth of 3cm? Is there anything to find that out?

[sciencebuddy]

Hi Scott,
I'm not very familiar with this topic, but I did a little bit of research on wikipedia
link: http://en.wikipedia.org/wiki/Acoustic_resonance#Closed

From what I could discern, the equation to determine the resonance frequency of a rectangular box is

f = (v/2) x √[(l/Lx)^2 +*(m/Ly)^2 + (n/Lz)^2)]

where
v = speed of sound (340 m/s)
Lx, Ly, Lz = dimensions of the box
l, m, n = non-negative integers of the dimensions of the box

Sorry I can't be of any more help!

-Daniel

[Craig_Bridge]

the equation to determine the resonance frequency of a rectangular box is

A more accurate statement would be "The equation to approximate the resonant frequency of air in a rectangular box is:"

I'm gonna go out on a limb here. Are there any equations to determine the resonance if you know the dimensions of the material being used? For example, a block of wood with a length and width of 12cm., and a depth of 3cm? Is there anything to find that out?

When it comes to resonance of solids, the density of the material and the elastisity of the material makes a significant difference for equally shaped and sized samples.

There are also multiple "modalities" of vibration. For example, if you firmly attached the entire perimeter of the piece you describe to something very stiff, then the vibrational modes available would all involve deflection of the center with respect to the perimeter. If you only attach one edge to something very stiff, and allow the opposite edge to be completely free in air, you have another vibrational mode that can occur. If it were suspended by a thread attached a hole near the corner, it would have a totally different set of boundary conditions.

The equations that describe vibrations are "boundary value" problems. Because the boundary constraints significantly effect the answers, deriving and publishing results to predict resonance frequencies for a given set of boundary constraints maybe mentally challenging but isn't very useful to solve real world problems except in a few common cases.

The equations (in the Wikipedia article referenced) for air and strings with some specific boundary conditions are useful because they come up in musical instrument, speaker design, air handling equipment and ductwork, and wire suspension designs that have enough common use cases to warrant their publication.

For your simple block of wood (suspended by a thread per my addition to the resonance problem definition), the type of wood will significantly alter the result. A piece a walnut is denser than a piece of spruce and both have different grain patterns (twisted vs straight) so they will sound differently when struck. Instead of cutting the blocks with the grain, cut them at 45 degrees to the grain so that it runs from one corner to the other instead of parallel to one side and you get a slightly different resonance. A vener grade solid birch plywood and a solid piece of birch would sound differently because of the alternate grain layer orientation of the plys. Effectively, each of the glue layers of the plys is a boundary. The growth rings are also boundary conditions so a piece of quarter sawn wood vs a simple band saw cuts from the center and edge will all have slightly different resonant frequencies and the differences will be greater for long thin pieces even though the grain is going the same direction in these pieces.

[edneu3]

As you can see from the last reply from Craig, the computation of the resonant characteristics of objects can be very complicated.

In industry, it is often very important to know the resonant characteristics of objects. One important reason is that as surfaces of objects resonate, they emit acoustic energy - sound. I think that's exactly what you are trying to predict with your block of wood. Sound emitting characteristics of consumer products is very important in today's world. People expect their products to be quiet. So designers of those products must understand the resonant characteristics of them.

In my company, we make high technology devices that are used in homes. They are expected to be very quiet. When we design the devices, we use very highly sophisticated computer models to predict resonances of the complex parts making up our products. These models are generally referred to as "finite element" models. They allow the designer to see how the objects resonate. These models can predict the "modality" that Craig mentioned. Here is a nice summary of finite element modeling (FEM), on Wikipedia: http://en.wikipedia.org/wiki/Finite_element_analysis. You can see the modeling can become quite elaborate and complicated.

One property of materials is how well they "transmit" sound. This is quite different from resonance, but very important. It is something of great importance and architect must keep in mind when designing a building, or when engineers are trying to build a more quiet automobile. You can learn something about it by visiting the web site: http://squ1.org/wiki/Sound_Transmission.

Good luck.

Ed

[scotta740]

Thanks! This helps a lot!!!