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A thermostat on the wall of your house keeps track of the air temperature. This simple approach is of little use in the large volume of a covered sports stadium, but there are systems that determine an average temperature of the air in a stadium by measuring the time delay between the emission of a pulse of sound on one side of the stadium and its detection on the other. Explain how such a system works.

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Answer and Explanation:

In any material medium, the speed of sound is dependent on the temperature of that medium. So, air being the material medium for the propagation of sound waves across the stadium, is no exception. The distance across the stadium should be known, to give the path Iength of the sound. This Path Iength is then taken and divided by the time between the emmision and detection of the pulse to obtain speed of sound. After knowing the speed of sound, One can determine The corresponding temperature either by calculation or referring to a Chart.

The calculation goes thus:

v = √(γ.R.T/M)

γ = 1.4

R = 8.314 J/(mol.K)

M = 0.029 kg/mol

T [K] → θ = T - 273.15 [°C]

Hope this Helps!!!

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