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

Question

Physics

Cannon

14 March, 01:16

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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Alessandra Gates · Answer 1

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