Inverse Variation

Question

The pitch of a musical note varies inversely as its wavelength. If a tone has a pitch of 440 vibrations per second and a wavelength of 2.4 feet, find the pitch of a tone that has a wavelength of 1.6 feet.

Answer 1

Because wavelength and pitch (frequency - note the units are vibrations, or waves per second) are inversely related, the below will work if we assume the speed of sound in air is constant (although these values seem a bit off for speed of sound).

P x W = P x W

440 x 2.4 = P x 1.6

P = 660 vibrations per second.