A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as 344 m s^–1.

When determining the wavelengths of sound waves corresponding to frequencies of 20 Hz and 20 kHz in air, we utilize the formula:

Wavelength(λ) = (Speed of Sound(v))/(Frequency (f))

Given:
Speed of sound in air (v) = 344 m/s
Frequency for the lower limit (f_low) = 20 Hz
Frequency for the upper limit (f_high) = 20,000 Hz (20 kHz)

1. For 20 Hz (lower limit):
The wavelength at 20 Hz:
λ_low = (344 m/s)/(20 Hz) = 17.2 meters

2. For 20 kHz (upper limit):
The wavelength at 20 kHz:
λ_high = (344 m/s)/(20,000 Hz) = 0.0172 meters = 17.2 millimeters

Hence, the typical wavelengths of sound waves in air corresponding to 20 Hz and 20 kHz are:
– 17.2 meters for 20 Hz
– 17.2 millimeters (or 0.0172 meters) for 20 kHz