The range of human hearing extends from approximately 20 Hz to 20,000 Hz. Find the wavelengths of these extremes at a temperature of 2°C.
20 Hz?
20000 Hz?
To find the wavelengths of the extremes of human hearing at a temperature of 2°C, we can use the formula:
Wavelength = Speed of Sound / Frequency
First, let's calculate the speed of sound at 2°C.
The speed of sound in air can be given by the formula:
Speed of Sound = 331.5 m/s + (0.6 m/s/°C) × Temperature
Substituting the given value of temperature (2°C), we have:
Speed of Sound = 331.5 m/s + (0.6 m/s/°C) × 2°C
= 331.5 m/s + 1.2 m/s
= 332.7 m/s
Now, let's calculate the wavelengths.
For 20 Hz:
Wavelength = Speed of Sound / Frequency
= 332.7 m/s / 20 Hz
≈ 16.64 meters
For 20,000 Hz:
Wavelength = Speed of Sound / Frequency
= 332.7 m/s / 20,000 Hz
≈ 0.016635 meters or 16.635 mm
Therefore, at a temperature of 2°C, the wavelength of 20 Hz is approximately 16.64 meters, and the wavelength of 20,000 Hz is approximately 0.016635 meters (or 16.635 mm).