Speed of sound versus temperature The speed of sound in air can be calculated by

Question

Speed of sound versus temperature The speed of sound in air can be calculated by v = squareroot B/rho. In air, B is related to the air pressure and rho is the air density. Under constant pressure, the temperature dependence of the speed of sound in air is through the density. At T = 273 K (0 degree C), the speed of sound was calculated in class to be 331 m/s. Let rho = m/V and rho_o = m/V_o be the densities of air at temperature T and T_0 = 273 K respectively. Here, m is the mass of air in volume V at temperature T and V_0 at T_0 = 273 K. Using Charles' Law, which states that the volume of gas is proportional to the temperature, we have V/V_o = T/273 K. Show that the ratio of the speed of sound (v) at temperature T to the speed of sound (v_0) at 273 K is given by v/v_o = squareroot T/273 K. Express temperature T from Kelvin to Celsius and plot v against temperature T(degree C) in the range from -10 degree C to 20 degree C. Compare your graph with the one given in Figure 14-5.

Explanation / Answer

v/v0

= (0/), pressure is constant

= (V/V0), since = m/V and mass is constant

= (T/273)

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