What determines what pitch an object such as a bell or tuning fork produces when struck? I have heard that the box in the "king's chamber" of the great pyramid at Giza is tuned to 438 Hz. I know that in hand-bell choirs, the bigger the bell, the lower the tone, but I have noticed that size does not seem to be the determining factor in a bell's tone.
Acoustics – What Determines the Pitch of a Resonant Object?
acoustics
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I will go mostly with Chad's argumentation. Larger equals slower, which should excite relatively more low frequency sound. Also note that the larger the blast (hopefully) the further away the observer is. And air is not a perfectly elastic acoustic medium, some energy is lost, and the higher frequencies attenuate quicker than shorter, so distance will selectively filter out the higher frequencies.
Also, note, explosion usually means detonation. A detonation is an exothermic reaction which spreads by the compression (adiabatic) heating from the shockwave, and the chemical energy maintains the shockwave. A shockwave is essentially a highly nonlinear soundwave, and as the overpressure decays with distance from the source is will grade into a soundwave. Fireworks (pyrotechnics) are not explosives, but are the (relatively) slow reaction of chemicals (combustables, and an oxidizer) due to heat. Fireworks may generate shockwaves in air, if the package ruptures at sufficiently high pressure. Likewise volcanic blasts are not detonations, but shockwaves formed by the escape of high pressure gas.
If an explosion is fast compared to the sound frequencies the detector is sensitive to (probably human ears in your case), then we might be able to model the explosion as a delta-function in time. A delta function should equally excite all frequencies, so it should be a simple matter of distance attenuation of sound waves.
An explosion close to a solid surface, creates an amazing effect I've heard called a mach-stem (although wikipedia does not produce anything useful for this term). In any case, at fixed distance the near surface shock wave is much stronger than the shockwave at height above ground. In essence the ground effect part of the shockwave weakens roughly only as 1/R rather that the 1/R**2 one would expect for a free air spherical blastwave. I don't know what effect this has on the sound spectrum (pitch), but you need to be at a much larger standoff distance from a near groundblast than from a samesized high altitude blast because of it.
A few observations.
First - if you record sound for a short time, the bandwidth of the sample will result in a smearing of the peaks. This only really matters if the sample is very short - with a 1 second sample you would have 1 Hz resolution, but if you sample for 0.01 second, the bandwidth is 100 Hz.
Second, you are using a scale that is quite compressed in the region of interest. That again makes me wonder whether you have not set up your sampling to be optimal for the frequencies of interest.
I have used a cheap iPhone app in the past to record sounds (Signal Spy - I am not connected to the product) and get an idea of their spectral content. I just played a simple scale on my guitar, and got the following (time along the horizontal axis, frequency vertical, intensity shows what frequencies are detected):
I have the feeling there's a problem with the labels on the logarithmic scale, but you can clearly see the fundamental and its harmonics; they are much better resolved than in your case.
This means that either your frequency is not constant, or your recording settings are very much not optimal for the task. Perhaps you can comment on the settings you used, and we can figure out how to get similar results for you. You used the words "a short region of the recording with minimal resonance was used..." - I wonder if your recording window was too short. I also wonder what windowing technique you used. When you do frequency analysis, you don't simply do the Fourier Transform of a snippet of sound - because if you do, you will generate a bunch of frequency content due to the way the signal "cuts off" at the start and end of the recording. Instead you need to apply an apodizing window (Hamming or Hanning window, usually) to get rid of extraneous peaks, and get cleaner frequency peaks.
If you have a pitch generator, the most accurate thing you could do would be to play the known pitch and slowly ramp it until the guitar string started to resonate. That works very well... as the resonance width is quite narrow. You would be able to determine the frequency within a fraction of a Hz (assuming your pitch generator produces enough output - perhaps you play it through a microphone and amplifier into a decent speaker).
Best Answer
When an object resonates, it will have a tendency to vibrate in a characteristic way (it's normal modes) to produce sounds at its characteristic frequencies, of which there may be more than one. Theses frequencies are basically a function of the geometry of the object, as well as the mass density and 'stiffness' of the material used. For example, an empty bottle will produce a characteristic pitch when air is blown across the top (similar to a flute). The bottle's length sets up the characteristic wavelength of the pitch produced. Half-filling it with water will produce the same pitch an octave higher (ie: half the wavelength). The pitch produced is also a function of the density and velocity of air. Blowing harder (higher velocity) can produce a different (alternative) mode of oscillation with different pitch.
In the case of a tuning fork, there is usually just one characteristic pitch (normal mode), which is a function of the density of the fork material, its characteristic length, cross-sectional area, as well as its 'stiffness'. A heavier (higher density) metal will oscillate slower and have lower pitch than a tuning fork made of a lighter metal. A longer tuning fork will also produce a deeper pitch (longer wavelength), all else being equal. Using a 'stiffer' material (a material with higher Young's modulus which does not 'stretch' or 'bend' as easily) will tend to produce a higher frequency pitch.