Humans can hear sound frequencies ranging from about 20-20000 Hz. What is the shortest wavelength humans can hear (assuming sound travels at 343m/s)
f = 1/T = 20,000 so T = 1/20,000
distance = speed * time
L = 343 T
L = 343/20,000
L =. 01715 meters or about 1.7 centimeters
To determine the shortest wavelength that humans can hear, we need to know the corresponding frequency. In this case, the highest frequency that humans can hear is 20,000 Hz.
The formula to calculate the wavelength is:
Wavelength (λ) = Speed of Sound (v) / Frequency (f)
Given that the speed of sound (v) is 343 m/s and the frequency (f) is 20,000 Hz, we can plug these values into the formula:
λ = 343 m/s / 20,000 Hz
Calculating this, we get:
λ = 0.01715 meters
Therefore, the shortest wavelength that humans can hear, assuming sound travels at 343 m/s, is approximately 0.01715 meters or 1.715 centimeters.