Scaling geometry by eta requires dividing frequency by eta in air

Evidence

The scaling works like this: Take a situation with given wavelength and size of objects, and then scale every length by some factor η—for example, η = 2—enlarging everything in the picture by a factor of 2, including any objects and the waves themselves, which increases their wavelength by a factor of 2 also. Since air is the propagation medium both before and after scaling, the speed of sound c must remain fixed. Every dimension of the objects increases by a factor of η, and since f = c/λ with c unchanged, the frequency decreases by the same factor, changing according to fnew = fold/η, and the wavelength according to λnew = ηλold. — Eric J. Heller, Why You Hear What You Hear- An…, 599

Categorization

• DEFINE: Precise statement of how the similarity/scale-invariance principle works with sound in air.