Question: Which musical instrument sounds the most like farts?
Short answer: A tenor trombone.
Long answer: We have previously examined the sound frequencies of farts and found that the dominant frequencies are in the range of 100 – 500 Hz, with a prominent peak around 260 Hz. This feature of fart sounds is so reliable that it allows us to determine whether a fart sound is real or fake. We have proposed that the consistency of fart sounds is attributable to the relatively simple configuration of the human rectum: Acoustically, it is basically a tube that is closed at one end. In this sense it is similar to brass instruments like tenor trombones, which in fact produce a similar range of frequencies.
Any tube that is closed at one end has a characteristic acoustic property: It produces a fundamental frequency and odd harmonics of this frequency. So if the fundamental frequency is 100 Hz, there should also be sound at 300 Hz, 500 Hz, etc. This is a consequence of the interaction between the tube and the sound wave, and musicians often call the higher frequencies “overtones.” Mathematically, the sound frequencies are:
where n is constrained to be an odd number. The power at each frequency decreases with n.
Given that farts have peak frequencies around 250 Hz, we can predict that they will also have power at odd-harmonic frequencies near 750 Hz and 1250 Hz. Here is the average power spectrum of 356 farts:
We see that, indeed, the third harmonic is present at 764 Hz, which is about 3 times the frequency of the main peak, at 258 Hz. There are also smaller peaks at higher odd harmonics (1308 Hz and 1804 Hz).
These overtones are likely to be part of the acoustic experience of a fart, because removing them changes the sound quality quite significantly. Here is a typical fart:
Here is the first harmonic by itself:
And here is the third harmonic by itself:
Neither is sufficient to capture the rich acoustics of fart sounds, which must depend on the various overtones, as well as variations in the aperture over time.