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Ridiculously easy way to measure speed of sound?


Don Noon

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Edit 2023:  (Details on the last page of this thread) while this method and the calculations are still correct, the signal does not come from a compression wave travelling back and forth through the wood, but from the first longitudinal mode of vibration of the wedge (think about stretching a spring, and then throwing it up in the air).  There are 2 practical implications:  1) The nodal line of this mode is in the middle of the board, so holding it there will not damp the vibration.  2) The board has to be uniform cross-section to get an accurate reading.  If it is thicker at the middle than the ends, the reading will be high, and vice versa.  

I don't know why I didn't try this before. David Tseng's recent post about using a Lucci meter got me thinking (always a danger sign): why do you need ultrasonics? A whack on the end of a board should send a compression wave zinging back and forth in the wood (which has low damping), which might be measurable with a regular microphone. So I tried it on a ~1-m long board I had on hand, previously measured my "usual" way of taking length, width, thickness, mass, and first bending mode frequency.

I smacked the end of the board with a very light (few grams) hammer, and close-miked the opposite end. I got:

post-25192-1270180414.jpg

The highest peak is quite apparent at 2695 Hz, and the next highest peak is just about an octave above that (edit: makes sense... a non-sinusoidal impact wave should show harmonics).

Now taking 2 x length and multiplying by frequency gives me C=5286 m/s, which is only 2.5% off from what I calculated using the aforementioned 5 measurements the "old" way.

I also tried it on a 1-pc top billet. The highest peak was at 6669 Hz, corresponding to C of about 5200 m/s for the length of the billet. I haven't measured the billet the old way, because it's not rectangular and even. The end-smack method doesn't need a rectangular section, although it might get mucked up if the cross-section varies greatly.

Now, I'm not claiming this is absolutely iron-clad yet, as I have only just tried it out and don't have enough statistics and experience with the method. But it makes sense, and so far it looks like it works.

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Why not take a one metre board, fasten a piezo transducer on each end, feed the transducers into a dual channel storage scope or recording software. Strike one end of the board close to the transducer and compare the delay between the first and second transducer. Essentially a wooden delay line.

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Why not take a one metre board, fasten a piezo transducer on each end, feed the transducers into a dual channel storage scope or recording software. Strike one end of the board close to the transducer and compare the delay between the first and second transducer. Essentially a wooden delay line.

'Cuz I don't have all that stuff.

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[q

++++++++++++

Would you explain why this two modal spikes could tell the speed of the sound in this piece of wood ? (In an elementary level,

like levels of college or high school physics) Thank you. It is interesting to know.

Do you mean that a spike is a result of two waves collide at that point when two waves travel

in opposite directions? and then... Let say f (frequency), 1/f = time difference, length of the stick= 1 meter.

speed = distance/ time = l meter/ (1/f) so it is the speed. Right?

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[q

++++++++++++

Would you explain why this two modal spikes could tell the speed of the sound in this piece of wood ? (In an elementary level,

like levels of college or high school physics) Thank you. It is interesting to know.

Do you mean that a spike is a result of two waves collide at that point when two waves travel

in opposite directions? and then... Let say f (frequency), 1/f = time difference, length of the stick= 1 meter.

speed = distance/ time = l meter/ (1/f) so it is the speed. Right?

v=f x lambda

For the lowest frequency longitudinal standing wave on the bar, lambda = 2xlength of bar. For the next highest frequency, Lambda = length of bar.

So the lowest frequency = v/2L, the next highest frequency = v/L.

It's only easy to do this now because of the ready availability of free FFT software and cheap computers. I would imagine that a netbook plus a microphone probably makes a lucchi meter obsolete?

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When you smack the end of the wood, it starts a pressure wave travelling along the grain. When it gets to the other end, it reflects as a tension wave and starts back in the other direction. When it gets back to where it started, it reflects again as a pressure wave and repeats the process. Similar to when you slap your hand on the end of a long pipe. For low-damping media, such as good spruce (or air), this wave will reflect back and forth many times, with the period of the cycle determined by the length and the speed of sound (one period will take a trip to the end and back, or 2L/C). For our wood, the "reflection" at the ends will have a small displacement of air, i.e. it will make a sound wave. We can record and analyze the sound to get the frequency. Since F=1/T (F=frequency, T=time for one cycle), we can take T=2L/C, rearrange to C=2L/T, or using frequency, C=2LF.

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When you smack the end of the wood, it starts a pressure wave travelling along the grain. When it gets to the other end, it reflects as a tension wave and starts back in the other direction. When it gets back to where it started, it reflects again as a pressure wave and repeats the process. Similar to when you slap your hand on the end of a long pipe. For low-damping media, such as good spruce (or air), this wave will reflect back and forth many times, with the period of the cycle determined by the length and the speed of sound (one period will take a trip to the end and back, or 2L/C). For our wood, the "reflection" at the ends will have a small displacement of air, i.e. it will make a sound wave. We can record and analyze the sound to get the frequency. Since F=1/T (F=frequency, T=time for one cycle), we can take T=2L/C, rearrange to C=2L/T, or using frequency, C=2LF.

++++++

Yes. it makes sense. In order to return, the wave has to travel two lengths, ie. where 2L from.

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Another test. I have a top set from Rivolta, which I have not cut up (and therefore not yet measured the old way), and I was curious about its properties. The end smack method gives:

post-25192-1270213222.jpg

Showing a clear maximum peak at 5168 Hz. The board being .56m long gives C = 5168 x 2 x .56 = 5788 m/s. I expected this wood would have higher C than my low-density Engelmann, and it appears to be so.

Further, looking at the amplitude trace of one smack:

post-25192-1270213233.jpg

The 5168 Hz signal is quite clear, and decays with Q approximately 150. This is about the right Q for along-grain vibrations.

I can think of no alternative explanations for these measurements, other than the one already given. This all appears to hang together very coherently.

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Don, brilliant idea! and you've saved me 3 thousand bucks. I've contacted BowWorks and just about to tell them to order one Lucchi in. Now all I need are a plastic piezo film and the little notebook computer. I have cooledit and praat softwares in the computer for analysis. I think JohnCee's standing wave explanation is correct. To build up the standing wave, the geometric constraints would apply.

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... For our wood, the "reflection" at the ends will have a small displacement of air, i.e. it will make a sound wave. We can record and analyze the sound to get the frequency. Since F=1/T (F=frequency, T=time for one cycle), we can take T=2L/C, rearrange to C=2L/T, or using frequency, C=2LF.

Hi Don,

The speed-of-sound [s-o-S] math is straightforward when measuring "through air", however, there must be a difference between that and S-o-S "through the wood" and "along its surface". Perhaps what you're measuring is closer to S-o-S "along its surface" ???

Jim

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Excellent idea!

I am trying to duplicate your results with the limited equipment that I have. Here is picture of a spruce top. I placed the mic next to one end of the board as it rests on a table and hit the other end with a two types of light hammers. My audacity log spectrum is not as clear as yours. I used the highest peak which was 6886 hz. Then v = 2 f L or 2 (6883) (.43) which gives 5919 m/s which seems a bit high.

post-24376-1270225945.png

I tried this with a finished top plate (f-holes cut no bass bar) and got mixed results. I got a lot of frequencies and was not sure which one to use. Any recommendations on how setup the mic, hammer and top in order to measure the velocity of finished tops??

post-24376-1270227046.jpg

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Excellent idea!

I am trying to duplicate your results with the limited equipment that I have.

It doesn't get much simpler than what I have:

post-25192-1270228516.jpg

Try balancing the plate on a soft eraser or similar. Friction with the table might disturb things.

I don't think this would work well with a finished plate... too much non-straightness, out-of-plane effects, non-planar end reflections, etc.

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I tried this with a finished top plate (f-holes cut no bass bar) and got mixed results. I got a lot of frequencies and was not sure which one to use. Any recommendations on how setup the mic, hammer and top in order to measure the velocity of finished tops??

I think it would work better if you use a contact microphone or a plastic piezo film attached with masking tape. A finished violin top can vibrate in so many different ways. There probably isn't any longitudinal standing wave because the the edge is thin and curved. I think this is the situation where Lucchi meter has the advantage.

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The highest peak is quite apparent at 2695 Hz, and the next highest peak is just about an octave above that (edit: makes sense... a non-sinusoidal impact wave should show harmonics).

Now taking 2 x length and multiplying by frequency gives me C=5286 m/s, which is only 2.5% off from what I calculated using the aforementioned 5 measurements the "old" way.

What was the 'old way' calculation found to be in m/s?

Was it 2.5 % higher or lower?

Thanks

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I've been trying to replicate this all day, with different pieces of wood and different "hammers", and can't. Anyone get success?

I was able to get some ball park figures that are in the right range but we need to standardize the experiment. What Don shows in his pictures is the following ( I think )

1. Audacity 1.3.12 (beta)

2. Simple MS microphone held very close to the end of the wood

3. Simple light weight metallic hammer with a wire handle

3. Wood placed on some mat

4. Press the Audacity record button and hit the end other end several times. Press stop

5. Pick your "best" click and perform the Analyze just that part of the wave form

6. Select Analyze, Plot Spectrum, Size 2048, and Log axis

Don can correct these parameters or make better suggestions.

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I just got a distinct peak at 5407 for spruce 433mm long. Is this in the ball park?

I tried it both with a mic and a piezo strip. The piezo produced an easier to find, and less cluttered peak, probably because it can be oriented to be most sensitive to vibrations on one axis.

One thing I noticed is that the frequency will be slightly different depending on how the piece of wood is supported. It was 5407 resting flat on a bench, and 5334 held in my hand. If that's enough difference to matter, I guess one would need a consistent test procedure.

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I've been trying to replicate this all day, with different pieces of wood and different "hammers", and can't. Anyone get success?

I can't tell; it seemed to work great every time I tried it. There might be something in the smacking technique... get a fast, sharp tap, letting the "hammer" bounce off the wood quickly. I also think the "hammer" has to be fairly light, not much more than a few grams. Light weight, high velocity. I showed the photo of what I used, and it ain't fancy.

I also think that skinny (half of a 2-pc top) might work better than a wide (1-pc top) slab. The smack is necessarily localized at one point, and sideways spreading of the wave might affect the measurement.

I just got a distinct peak at 5407 for spruce 433mm long. Is this in the ball park?

That looks awfully low... C=4682 is mighty low for spruce, unless it's soaking wet.

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Here's a link you may find useful:

Sylvie

How the block is held should be important. A xylophone has resonators (blocks, pipes, whatever) which lie in from the ends. The rest points become nodes for vibration. I think that to measure the speed through the piece of wood, you need to support it the ends (only.)

But what do I know...

Doug

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