# Sound propagation in solids

1. Sep 25, 2007

### jacketyjack

Hi all,

I was wondering whether someone can help/guide me. I am doing a project that involves sound propagation in solids. Basically, I have two microphones placed on a surface (say a piece of wood). Then, when a person taps on the surface I can detect the tap and determine the amplitude of tap at both microphones. I then use the two amplitudes (listeners) to triangulate the position of the tap on the surface. The rough schematic of the arrangement is attached (Board.jpg). Note that the tap can be anywhere on the surface. As such, I want to create a mouse-type device the moves the mouse the location corresponding to the location where the person tapped on the surface. The equations/model I am using is exponential decay of sound in solids as follows:

For microphone 1:
$$A_{1} = A_{0}e^{-\alpha_{1} d_{1}}$$

The same for microphone 2:
$$A_{2} = A_{0}e^{-\alpha_{2} d_{2}}$$

Where:

$$A_{1}$$,$$A_{2}$$ are the amplitudes of the tap as heard by mic 1 and 2 resp.
$$A_{0}$$ is the amplitude of the tap before any decays happen i.e at the tap location
$$\alpha_{1}$$,$$\alpha_{2}$$ is the decay constant of mic 1 and 2 resp, and no they are not exactly the same since mic1 and mic2 are different in terms of electronics.
$$d_{1}$$,$$d_{2}$$ are the distances to the tap location from mics 1 and 2 resp.

Thus, I calibrate the setup and determine the alphas, then I probe the mics regularly to determine when a tap occurs and when it does I use the equations above to determine the distance of the tap from each mic using the amplitudes.

I have tried to apply this scheme and to some extent it works. THE ONLY problem, which I hope someone will help me figure out, is how to make the equations independent of how hard the person taps. Thing is: if the person taps harder than usual at a far location, the mics will pick up higher amplitudes and therefore the computation will determine that the tap occured closer than it actually did. The reverse is also true (i.e. softer tap at closer distance = mics think tap is farther away)

Some leads that I have: $$A_{0}$$ , $$A_{1}$$ and $$A_{2}$$ depend wholly on how hard the person taps. So if I could somehow compute how hard the person has tapped (would this be intensity or power anyway?), then I can determine the right $$A_{0}$$ to use and the equations will produce the exact location perfectly. Problem: how do I determine the power/intensity of the tap?

Leads on determining power: In the current scheme, I am treating $$A_{1}$$ and $$A_{2}$$ totally separately. And therefore each mic only has limited information. But if I could somehow use BOTH amplitudes together to compute tap location/power/intensity, I think this would solve it.

Any help would be greatly appreciated.

Jack.

#### Attached Files:

• ###### Board.JPG
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Last edited: Sep 25, 2007
2. Sep 25, 2007

### f95toli

You know the distance between the microphones and the speed of sound in wood.
I don't think you need to the amplitudes.

3. Sep 25, 2007

### jacketyjack

Yes but what I don't know is the location of the tap. Note that the tap does not occur at a fixed location but varies in time. I need the amplitudes to probe the position of the tap. Otherwise how else?

4. Sep 25, 2007

### f95toli

Difference in arrival time tap-> the two microphones?

5. Sep 25, 2007

### Loren Booda

Wood may be too heterogeneous for your needs.

The suggestion f95toli gave should work in time dependent situations. It would be much more reliable than working with amplitude. His makes the situation independent of how hard the person taps.