Some studies indicate that the upper frequency limit of...

Some studies indicate 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 this is so, what is the diameter of the eardrum of a person capable of hearing $2.0 \times 10^{4} \mathrm{Hz}$ ? Assume $378 \mathrm{m} / \mathrm{s}$ is the speed of sound in the ear.

Key Concepts

Speed of Sound

The speed of sound is the rate at which sound waves propagate through a medium, and it depends on the medium's physical properties such as density and elasticity. In problems involving sound propagation, the known speed is used along with frequency to determine the wavelength of the sound, which in turn can relate to other physical dimensions in the system.

Wave Equation (v = f?)

This fundamental relationship in wave mechanics links the speed (v) of a wave to its frequency (f) and its wavelength (?). It allows us to calculate one of these quantities if the other two are known. In acoustics, this equation is used to relate how fast sound travels in a medium to the pitch (frequency) and the spatial extent (wavelength) of the sound waves.

Frequency

Frequency represents the number of complete oscillations or cycles of a wave that occur in one second and is measured in Hertz (Hz). It determines the pitch of sound in acoustics, and higher frequencies correspond to higher pitches. This concept is crucial in understanding how the characteristics of sound waves relate to physical dimensions, such as the size of the eardrum.

Wavelength

Wavelength is the spatial period of a wave—the distance over which the wave's shape repeats—and is inversely related to frequency when the speed of the wave is constant. In the context of acoustics, knowing the wavelength of a sound wave helps in analyzing how physical structures, like the eardrum, interact with and respond to sound.

Transcript

Please give Ace some feedback