Some studies suggest that the upper frequency limit of hearing is determined by the diameter of the eardrum. the wavelength of the sound wave and the diameter of the eardrum are approximately equal at this upper limit. if the relationship holds exactly, what is the diameter of the eardrum of a person capable of hearing 22,600 hz? (assume a body temperature of 37.0°c.

The relationship that is connecting the wavelength of the sound and it's frequency is v=λ*f where v is the speed of the sound and its around 333 m/s, λ is the wavelength and f is the frequency. If we manipulate the formula to get λ it should look like this: λ=v/f. Now we plug in the numbers and get: λ=333/22600 = 0.0147345 m = 1.47 cm. So if the wavelength and the diameter are equal, the diameter of the eardrum should be 1.47 cm.