Question

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.

Answer 1

The diameter of the eardrum for a person capable of hearing 22,600 Hz is approximately 0.0152 meters.

Step-by-step explanation:

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. To calculate the diameter of the eardrum for a person capable of hearing 22,600 Hz, we can use the formula:

Diameter = Speed of Sound / Frequency

Using the given speed of sound in air of 344 m/s and the frequency of 22,600 Hz, we can substitute these values into the formula to find:

Diameter = 344 m/s / 22,600 Hz = 0.0152 m

Therefore, the diameter of the eardrum for a person capable of hearing 22,600 Hz is approximately 0.0152 meters.

Answer 2

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.