Question: Why do all farts have the same peak sound frequency?
Short answer: Rectal acoustics.
Long answer: In recent posts, we have been concerned with the observation that there is a remarkable consistency in sound frequency across our database of 2000 farts. This consistency has made it possible to detect farts in sound recordings and to exonerate people accused of farting in public. But many readers have asked why the consistency among fart sounds should exist in the first place.
One concern is that it is an artifact of our recording procedures. To control for this possibility, we downloaded farts from a neutral, third-party site. The time-frequency plots below indicate that these farts have the same signature sound frequencies as in our database, with the characteristic peak in the 200 – 300 Hz range:
Thus, the universality of the acoustic signature of farts suggest a more interesting explanation, namely that is caused by some feature of human anatomy.
In all likelihood fart sounds represent an acoustic resonance caused by gas moving through the rectum. If we model the rectum as a tube that is closed at one end, the resulting sound frequency is given by:
where f is the sound frequency, v is the speed of sound (343 m/s), L is the length of the tube, and d is the diameter of the tube. Typical estimates suggest that the human rectum is about 20 cm long and the anal canal another 3 cm, while the diameter of the passage reaches about 6 cm. With these numbers, we can calculate a resonant frequency of 320 Hz, which is reasonably close to the average peak fart frequency of 272.1 Hz in our database. The source of the small discrepancy remains unclear.
This observation is generally consistent with the notion contained in Dante’s Inferno, that farts obey the same physics as musical instruments:
“Along the left-hand dike they wheeled about;
But first had each one thrust his tongue between
His teeth towards their leader for a signal;
And he had made a trumpet of his ass.”
The above equation applies to both musical instruments and farts, and it suggests that the primary determinant of sound frequency should be the length of the tube through which air is forced. To test this idea, we obtained a sample of a fart produced by a hippopotamus (Hexaprotodon liberiensis):
Here is the time-frequency histogram of the hippo fart:
The peak frequency occurs at 195 Hz, substantially lower than the vast majority of human farts. Thus, it appears that hippopotamus anatomy is sufficiently different from human anatomy to cause a significant shift in the sound frequency of farts.
We were unable to find reliable estimates of the length of the hippopotamus rectum, but qualitative descriptions suggest that it is considerably longer than that of the human rectum (Chapman, 1881). Indeed, by substituting the dominant hippo frequency of 195 Hz into the equation above, we arrive at the conclusion that the hippopotamus rectum is 43.9 cm in length.