A hypothesis says the upper limit in frequency a human ear can hear can be determined by the diameter of the eardrum, which should have approximately the same diameter as the wavelength at the upper limit. Using the hypothesis what would be the radius of the eardrumfor a person able to hear frequencies up to 18.5 kHz?
...should I be finding the amplitude of the wave which would equal the diameter..if yes then how do i go about doing this?
It says it itself: drum diameter = wavelength for 18.5kHz
wavelength = V/f = 330/18500 (metres)
or 1.78 cm
To find the radius of the eardrum using the hypothesis, we need to utilize the equation that relates the wavelength of a sound wave to its frequency and speed of sound. The equation is given by:
λ = v/f
where:
λ is the wavelength,
v is the speed of sound in air, and
f is the frequency of the sound wave.
The speed of sound in air is approximately 343 meters per second at room temperature.
To find the radius of the eardrum, we need to first find the wavelength of the sound wave corresponding to a frequency of 18.5 kHz (18500 Hz).
Step 1: Convert the frequency to Hertz:
Frequency = 18.5 kHz = 18500 Hz
Step 2: Use the equation to find the wavelength:
λ = (343 m/s) / (18500 Hz)
Step 3: Calculate the wavelength:
λ ≈ 0.0186 meters (or 18.6 mm)
According to the hypothesis, the diameter of the eardrum should be approximately equal to the wavelength at the upper limit. So, to find the radius (assuming the eardrum is circular), we can divide the diameter by 2:
Radius ≈ 0.0186 meters / 2
Radius ≈ 0.0093 meters (or 9.3 mm)
Therefore, if the hypothesis holds true, the radius of the eardrum for a person able to hear frequencies up to 18.5 kHz would be approximately 9.3 mm.