Question: Do fart sounds vary across the animal kingdom?
Short answer: Yes.
Long answer: We have seen that the peak sound frequency of human farts is remarkably consistent across farts and, moreover, that the sound frequencies of farts can be predicted from the typical length of the human rectum.
These findings lead to an interesting prediction, based on the laws of allometric scaling. In general, as animals increase in size, different body parts can be expected to expand at different rates. Weight depends on size in 3 dimensions, while the surface area of the skin, for example, is a two-dimensional quantity. Galileo was the first to discuss this principle, in his Discourses and Mathematical Demonstrations Relating to Two New Sciences.
A thorough treatment of the topic was provided by D’Arcy Thompson in his classic On Growth and Form.
This principle provides a way of predicting the length of an animal’s rectum from its weight:
L=kw1/3
Here L is the length of the rectum, w is the weight, and k is a constant. And since the peak sound frequency of farts is proportional to L, it follows that it should therefore be proportional to w1/3 as well. To test this hypothesis, we downloaded the fart sounds of various animals and analyzed their frequency content. Here is the result:
Each red dot corresponds to a different species, and the black line shows the linear fit between the cube-root of weight and the peak sound frequency of each animal’s fart. The linear fit has an R2 value of 0.81, indicating that the expected relationship does obtain and that it is for the most part, isometric. From the fit, we obtain a general scaling law for the frequency f of fart sounds:
f=332.9-16.9w1/3
The generality of this law allows us to extrapolate it to other species, even those that are now extinct. We can estimate, for example, that a Tyrannosaurus fart would have a peak frequency of 9.7 Hz.