The range of human hearing extends from approximately 20 Hz to 20,000 Hz. Find the wavelengths of these extremes at a temperature of 12.0°C.20 Hz m20,000 Hz m
Question
The range of human hearing extends from approximately 20 Hz to 20,000 Hz. Find the wavelengths of these extremes at a temperature of 12.0°C.20 Hz m20,000 Hz m
Solution
To find the wavelengths of these extremes, we need to use the formula for the speed of sound, which is given by:
v = 331.4 + 0.6T
where v is the speed of sound in m/s and T is the temperature in °C.
First, let's find the speed of sound at 12.0°C:
v = 331.4 + 0.6 * 12.0 = 337.6 m/s
Next, we use the formula for the wavelength, which is given by:
λ = v / f
where λ is the wavelength in meters and f is the frequency in Hz.
For 20 Hz:
λ = 337.6 m/s / 20 Hz = 16.88 m
For 20,000 Hz:
λ = 337.6 m/s / 20,000 Hz = 0.01688 m
So, the wavelength at 20 Hz is approximately 16.88 meters and at 20,000 Hz is approximately 0.01688 meters.
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