Two observers are riding on a train traveling along a straight level section of track at the constant velocity,v. It is a windless day, so that the air/medium is at rest relative to the moving train. Relative to the train’s direction of travel one observer sits at the rear of a train car of lengthL, and the other observer sits at the front of the same train car. The windows and doors are closed, so the air molecules inside the train car share in the motion of the train car.

The rear observer is holding a flashlight and a clock, the front observer has nothing. They sit facing each other then she begins their thought experiment. She flashes the light towards the other observer and starts her clock at the same moment. When the other observer sees the flash of light he yells back at her. When the sound wave of his yell reaches her she stops her clock. The light signal is effectively instantaneous over this short distance so the duration of time she measures is for the sound wave to travel at the constant velocitycalong the lengthLto her ear. The speed of soundcis constant in that the emitter does not add any velocity to the sound wave due to the emitter‘s motion. She would then calculate the speed of the sound wave as c_{e}=L/ t_{e}, where t is the time measured inside the enclosed compartment. In this case the distance the sound wave travels is equal to L due to the forward velocity of the molecules matching the train‘s velocity. The time value measured should be as if the train were at rest.

Next, the two observers clamber up to the roof of the same train car and take their same positions at the front and rear of the train car. She begins the same experiment that they performed earlier but now they are exposed to the stationary air with the train moving through the air molecules at the constant velocity,v. She once again flashes the light signal and at the same moment starts her clock. He yells once again when he sees the signal then she measures the time for the sound wave to reach her ear. She then calculates the speed of the sound wave as c_{r}=L/ t_{r}, where t_{r}is the time measured on the roof of the enclosed compartment. In this case the distance the sound wave travels is less than L due to the air molecules having zero velocity as the train plows through them at the velocity v. The time value measured should be less than if the train were at rest.

If t_{e}does not equal t_{r}then has she measured two different values for the speed of sound,c? Is there a difference between measuring the time within the enclosed compartment where the air molecules have the velocity of the train, and measuring the time on the outside of the train car where the air molecules have a velocity of zero?