Compute the speed of sound waves in air at room temperature (T=200C) and find the range of wavelengths in air to which the human ear (which can hear frequencies in the range of 20 – 20,000Hz) is sensitive. The mean molar mass of air (a mixture of principally nitrogen and oxygen) is 28.8 x 10-3kg/mol and the ratio of heat capacity is ϒ = 1.40.

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27-06-2022
Physics

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Compute the speed of sound waves in air at room temperature (T=200C) and find the range of wavelengths in air to which the human ear (which can hear frequencies in the range of 20 – 20,000Hz) is sensitive. The mean molar mass of air (a mixture of principally nitrogen and oxygen) is 28.8 x 10-3kg/mol and the ratio of heat capacity is ϒ = 1.40.

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sp10925 sp10925 · Answer 1 · 2022-06-29T10:55:54+02:00

The speed of sound waves in air at room temperature T=20° is 344.035 m/s.

The range of wavelength in air to which the human ear (which can hear frequencies in the range of 20 – 20,000Hz) is sensitive is 17.20 m to 0.0172 m.

What is wavelength?

The wavelength is the distance between the adjacent crest or trough of the sinusoidal wave. The wavelength is the reciprocal of the frequency of the wave.

Wavelength λ = c/f

where c is the speed of sound wave.

Given the room temperature T = 20 +273 = 293K

The velocity of sound wave is given by

v = √(γRT/m)

where γ =1.4 , m = 28.8×10⁻³ kg/mol R = 8.31 J/K.mol

Substituting the values, we get

v = 344.035 m/s

Thus, the speed of sound wave is 344.035 m/s

The human ear can hear frequencies in the range of 20 – 20,000Hz.

The wavelength corresponding to 20Hz is

λ = c/f

λ = 344.035 /20

λ = 17.20 m

The wavelength corresponding to 20,000Hz is

λ = 344.035 /20000

λ = 0.0172 m

Thus, the range of wavelength is 17.20 m to 0.0172 m sensitive to human ear.

Learn more about wavelength.

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