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25 January, 10:38

The speed of sound at 0°C is 331.5 m/s. Calculate the speed of sound in the room at 20.0°C.

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  1. 25 January, 12:28
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    The speed of sound is defined as the rate wherein pressure waves would move through a certain medium. From the kinetic theory, we know that c is equal to square root of dP/dρ where c is the speed of sound. From the ideal gas law, we have P = ρRT/M from the expression PV = nRT. Then, it follows that dP/dρ = RT/M = (Rm) (T) where Rm is the specific gas constant.

    From the problem statement, we can calculate as follows:

    Rm = c^2/T = 331.5^2 / (273.15+0) = 402.3 J/kg. K

    Next, at the new temperature, we calculate the speed of sound as follows:

    c = squareroot ((Rm) T) = squareroot ((402.3) (273.15+10)) = 337.5 m/s
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