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Measuring the Velocity of Sound in wood - directly


catnip

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(2) Continue the old way: buy only lighter wood. When I am home, cut a piece of wood from the wedge to make bassbar, and measure the xylophone frequency and density.

more accurate results can be obtained by measuring several mode frequencies (place the accelerometer or microphone close to the end of the bar) using Audacity or similar, and plotting f(n) vs (2n-1)^2. The speed of sound can then be simply derived from the gradient of the straight line obtained.

Apologies if a similar method has already been suggested in an earlier thread.

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more accurate results can be obtained by measuring several mode frequencies (place the accelerometer or microphone close to the end of the bar) using Audacity or similar, and plotting f(n) vs (2n-1)^2. The speed of sound can then be simply derived from the gradient of the straight line obtained.

Apologies if a similar method has already been suggested in an earlier thread.

Not sure what f and n represent. Is f frequency? What is n?

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Is there some belief velocity of sound in wood trumps velocity of sound in Air? If one measures a "number" for velocity of sound in linear wood samples, how would that single number be used to improve Violin sound output ??

It seems with a complex-curved wooden corpus, curvature impacts sound transmission efficiencies at every point in a nonlinear manner.

Thanks,

Jim

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more accurate results can be obtained by measuring several mode frequencies (place the accelerometer or microphone close to the end of the bar) using Audacity or similar, and plotting f(n) vs (2n-1)^2. The speed of sound can then be simply derived from the gradient of the straight line obtained.

Apologies if a similar method has already been suggested in an earlier thread.

John,

Please give us some references to learn about this method. Does one need to have the dimensions of the bar and weight? What about requirements for supporting the bar?

Thanks,

JohnS

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FWIW if I recall correctly the maker of the Arcus carbon fiber bows says the claimed superior sound of Arcus bows is in part due to the faster speed of sound in the "sticks".

Isn't that like saying a tuning fork's resonant frequency is dependent on velocity of sound through its metal tines ?? :)

Jim

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John,

Please give us some references to learn about this method. Does one need to have the dimensions of the bar and weight? What about requirements for supporting the bar?

Thanks,

JohnS

Your bar should be suspended by threads attached at points about 20% of the total length from each end of the bar. These are the locations of the nodes of the fundamental transverse mode of vibration. The frequencies f(n) of the various modes of transverse vibration are given by:

f(n) = pi*v*K*(2n+1)^2/(8*L^2).

Here, v is the speed of sound, K is the radius of gyration of the bar, n is an integer: 1,2,3,...etc, and L is the length of the bar.

For a cylindrical bar, the radius of gyration K=radius/root2, for a rectangular bar, K=thickness/root12. When you measure the transverse vibrational frequency spectrum of the bar, you should see a series of peaks at increasing frequency, due to the (2n+1)^2 term.

If you plot the frequencies of these peaks versus (2n+1)^2 you should get a straight line of gradient pi*v*K/(8*L^2), from which the speed of sound v can be calculated. If you tap the centre of the bar and measure at the end you should see all the modes excited. If you measure in the centre you may have missing modes, since every alternate mode has a node at the centre.

Does this help?

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Your bar should be suspended by threads attached at points about 20% of the total length from each end of the bar. These are the locations of the nodes of the fundamental transverse mode of vibration. The frequencies f(n) of the various modes of transverse vibration are given by:

f(n) = pi*v*K*(2n+1)^2/(8*L^2).

Here, v is the speed of sound, K is the radius of gyration of the bar, n is an integer: 1,2,3,...etc, and L is the length of the bar.

For a cylindrical bar, the radius of gyration K=radius/root2, for a rectangular bar, K=thickness/root12. When you measure the transverse vibrational frequency spectrum of the bar, you should see a series of peaks at increasing frequency, due to the (2n+1)^2 term.

If you plot the frequencies of these peaks versus (2n+1)^2 you should get a straight line of gradient pi*v*K/(8*L^2), from which the speed of sound v can be calculated. If you tap the centre of the bar and measure at the end you should see all the modes excited. If you measure in the centre you may have missing modes, since every alternate mode has a node at the centre.

Does this help?

JohnCee,

Yes, that helps a lot. Have you actually tried it? I am wondering if the microphone will be able to pick up enough energy to get the correct answer. Or do you know anyone who has tried it?

Thanks.

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JohnCee,

Yes, that helps a lot. Have you actually tried it? I am wondering if the microphone will be able to pick up enough energy to get the correct answer. Or do you know anyone who has tried it?

Thanks.

I've done it with an accelerometer and it works very well. Never tried with a microphone. Might give it a try in the next week or so.

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I've done it with an accelerometer and it works very well. Never tried with a microphone. Might give it a try in the next week or so.

Easy enough... I just tried it with an Engelmann bass bar. Held with fingers at nodal point, tapped and miked at the end. I also held it at the center, and tapped/miked at the end to get the alternate nodes better (although they did show up clearly as peaks held at the other position with Audacity).

post-25192-1269371069.jpg

The "theoretical" line is what you'd get if all higher modes were exact, based on the actual measured mode 1. Looks like the higher frequency modes drop off slightly. In any case, it doesn't look that far off, and I'll just continue to use only mode 1 for my calculations of wood properties.

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Mike Molnar and John Cee,

Mike, I agree that one has an orthotropic material and a set of elastic constants. Along with bulk density. (9 of them for the special case of orientation of wood in a violin top)

John Cee: Is there anything else to know except these elsastic constants (not considering damping for the moment) ?

After that, won't the speed of a wave depend on the type of wave? And a transverse wave in a thin bar will depend on the thickness of the bar? I know this is true of a plate. I have asked my question a couple of times. You are a physicist.. will you please answer for me?

Would it be better to consider the [principal, longitudinal] modulus along with the density instead of all this radiation ratio? For the sake of the demonstration, please just consider an isotropic material.

Please answer this and don't pull any punches, you can't hurt my feelings.

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Easy enough... I just tried it with an Engelmann bass bar. Held with fingers at nodal point, tapped and miked at the end. I also held it at the center, and tapped/miked at the end to get the alternate nodes better (although they did show up clearly as peaks held at the other position with Audacity).

post-25192-1269371069.jpg

The "theoretical" line is what you'd get if all higher modes were exact, based on the actual measured mode 1. Looks like the higher frequency modes drop off slightly. In any case, it doesn't look that far off, and I'll just continue to use only mode 1 for my calculations of wood properties.

If I remember right, the theoretical expression that John Cee gave above is actually an approximate expression that becomes closer and closer to correct as n gets large. I don't think that n has to be very large for it to be pretty close to correct though. If this is the case that I'm remembering, the correct frequencies are obtained by solving an equation which is something like cos(x) = 1/cosh(x) . The 'exact' low n solutions have to be found numerically.

Also this is a 'thin beam' solution. Normally a beam is treated as thin if its thickness is 1/10 or less than the length. This is because for thick beams the rotational motion about the nodes will start adding significantly to the kinetic energy. Depending on the size of your bass bar blank it might be on the borderline of what is safe to treat as a thin beam. If you want to try things like measuring speeds of sound or elastic constants of wood strips then I think it's a good idea to keep the samples as long and thin as is practical. This will give you more modes (within audio frequencies) to plot a line against and make the thin beam approximation safe to use.

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In a homogeneous substance, the wave velocity for longitudinal and transverse vibration are the same. It is not that simple in anisotropic substance such as wood, particularly in the cross-grain direction. The transverse vibration involves shear. Therefore, ultrasonic method would give a higher value of c (vel. of sound).

I use the bassbar stock cut from the wedge for top and determine the fundamental mode frequency f (free-free end or xylophone mode).

f = 1.028 cH/L^2 or c = 0.973 fL^2/H

where L is the length, H thickness.

It's much more quicker to get the results in along and cross grain directions using ultrasound technique. There has been a great deal of advancement in recent years in ultrasonic NDT equipments development. There are many portable units on the market. To measure the "time of flight", all you need is a pulser-receiver circuit; many cheap ultrasonic thickness gauge can also display time of flight.

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Now all we need are sound samples of your violins. :)

Let me answer catnip's original post: Measuring c, any simple device there?

You don't need to spend 3 grands to buy a Lucchi meter, many ultrasonic thickness gauges will measure c if you enter the length, for example Panametrics 35 series thickness gauge, others will display time of flight. The cheapest (less than $200) such as

http://cgi.ebay.com/Digital-Ultrasonic-Thi...=item3a5910dfa6

costs less than the stone-age Hacklinger gauge. Cut a small cube of wood from your scrap violin wood. Sand all surfaces smooth. Measure the dimensions with a micrometer. Place the ultrasonic probe on it. Change the velocity setting (usually in 10 m/s step) until it displays the correct thickness you measured. Then the speed setting is the correct c in that direction. If you know how to re-program the microprocessor, you can make it to display time of flight which is the round trip time from one surface to the opposite and back. c=2L/t

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Let me answer catnip's original post: Measuring c, any simple device there? The cheapest (less than $200) such as

http://cgi.ebay.com/Digital-Ultrasonic-Thi...=item3a5910dfa6

Thanks David, this is exactly what I wanted to know. So conversely once the velocity of sound is determined then that device can be used to measure the thicknesses of a assembled violin ... dual purpose!!

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All this is very interesting. Have you ever given any thought to using extremely high speed cameras to visulaise what happens to a violin belly at varying speeds/frequencies? These cameras can be programmed to record at varying speeds ranging to multiple thousands of frames per second, lending themselves to any number of interesting experiments. So far as I know, they've not been used in this fashion, but I'm no expert.

For those who might be interested, there are a couple links:

Water balloon pricked with pin: water balloon

And for the more violent among us, a lengthy exploration of bullets and various targets.

The second is rather longer, and quite a bit more interesting. I understand these cameras can be rented. I long to see what you folks can come up with using this tool.

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Throw a little dust onto the top, and you've got yourself a Discovery Channel special.

One of my friends was experimenting with old surgical video cameras, because they give you a live feed without compression (loss of frames).

Some YouTube randomness:

click to 4:40 for the violin (interesting time stamp for the violin... 440... :))

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Unfortunately, the displacements are too small for this... that is why the 3D laser vibrometer was used, which is the appropriate tool to measure the motions of a vibrating violin.

What sorts of distances are we talking bout. Say for the maximum motion of a low mode at moderate playing volume? Also, could you tell me once again the units of a radiation ratio? I tried to look it up but cannot find it.

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Displacement naturally will vary inversely with frequency. According to the Strad3D animations, maximum displacements show a range of a few hundred nanometers at low frequency, down to 10's of nanometers (or less) at the upper ranges. I don't know how strong the driving force was compared to normal playing volume, but I expect it was comparable.

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