## Sound… of what

Striking a metal rod can create sound. How the rod emits sounds may depend on various factors, such as the way the rod is supported, material used to hit the rod, etc. But carefully listening to the sound we notice that there is a component with the lowest pitch.

Say the rod is of:

• length (L): 100mm = 0.1m,
• Young’s modulus (E): 197GPa,
• Poisson’s ratio ($\nu$): 0.3,
• density ($\rho$): 8000Kg/m^3.

Then wave velocity in the rod should be something like

$c = \sqrt{\frac{E}{\rho}} \approx 4962$ [m/sec].

Assuming free vibration (no fixed boundary), wave length of the fundamental mode should be

$\lambda = L \times 2 = 0.2$ [m].

Its frequency is then

$f = \frac {c}{\lambda} \approx \frac {4962}{0.1 * 2} \approx 24.8$ [KHz].

The frequency is way beyond the upper limit of my hearing.  So I am hearing sub-harmonics, or what?

Computer Programmer
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### 9 Responses to Sound… of what

1. Piers Williamson says:

FYI: Working on the basis of the sub-harmonic equation listed above, a field test was in fact conducted during the 1996 World Cup. It was found that French skulls were slightly less resonant than German when struck with metal rods. This was an unexpected result.

There was no discernable difference when struck with wooden rods. The wooden rods tended to break more on the French skulls than on the German. Again this was within the expected parameters.

Further tests are planned for the 2010 World Cup where the results will be triangulated with African skulls in accordance with the more traditional method.

NB: the above results were, however, subject to a certain degree of interference due to supra-harmonic screaming. Regarding the supra-harmonic effect, the French subjects were more harmonic than the German. This of course came as no surprise to anybody.

• azumih says:

do we have data from the games in South Africa?

• voodoo child says:

The latest results have finally been collated.

Unfortunately, the quality of data this time was less than satisfactory.
Two main factors were involved.
First, the small n. No violent head bopping occurred at or around the stadiums, therefore our research teams were not able to participate in what is technically known in Australian terminology as “a bit of biffo” without being observed. Some did attempt it further away from the grounds in the slum areas but have not yet returned. It seems likely that their white coats and clip boards hindered adequate environmental adaptation.

Secondly, the vuvuzela factor. This caused extreme interference with our recording devices and corrupted the samples.
The vuvuzela factor was mitigated at England matches, and one can clearly hear strains of “the referee’s a wanker” after the disallowed goal against Germany. Again, however, whilst this did promise to develop into a fertile testing environment, no such head bopping materialised.

The only statistically significant results we have were taken from on-the-pitch action during the final. We can thus tentatively suggest that Spanish heads thwack when hit by Dutch boots, whilst Spanish chests do not crack.

• azumih says:

Thanks a lot for your observations.
I heard that the vuvuzela sound can be filtered out, because the sound is rather band-limited in frequency. I may check the final with some filtering turned on to examine the thwack sound.

2. azumih says:

Being a Japanese, I am interested to see what is response of Japanese sculls like. Are there any data from ’96 games?

3. Piers Williamson says:

there was limited data for the response of Japanese skulls given the small n.

however, some data was collected during the 2004 Asian Cup. Chinese particpants found that because Japanese skulls are somewhat flat at the back the metal rods tend to slide off thereby deadening the overall impact, but not the satisfaction.

4. mf says:

something to do with what they eat?

5. azumih says:

Well, mine is fairly nicely flat. And my brother’s too. I do not know why.

6. Piers Williamson says: