Physics - Speed of Sound question

Question

Students sitting in the stands at an athletic competition 200 m from the starting line see the smoke from the starting pistol 0.6 s before hearing the sound of the gun. Assess how you could determine the air temperature from this information and make the calculation.

Answer 1

Work with the relation for the speed of sound in air.

a = √(γRT)

γ = specific heat ratio of air (look it up)

R = Universal gas constant (look it up) divided by the average molecular weight of air (look it up)

T = absolute temperature of the air = ?

T = a² / (γR)

a = distance / time = (200 m) / (0.6 s) = ? m/s

Plug in the values of a, γ, and R into the equation for T, in appropriate units.

Answer 2

The distance and the time allow you to calculate the speed of sound in the local conditions.

Look up the equation for speed of sound as a function of air temperature. This will allow you to determine the temperature.

https://en.wikipedia.org/wiki/Speed_of_sound#Dependence_on_the_properties_of_the_medium