The back wall of an auditorium is 29.0 m from the stage. If you are seated in the middle row, how much time elapses between a sound from the stage reaching your ear directly and the same sound reaching your ear after reflecting from the back wall?

0.29 m divided by the speed of sound.

You are 14.5 m from the stage and back wall. The reflected wave from the back must make a round trip of 0.29 m before reaching you.

what is the speed of the sound

About 340 m/s in air at room temperature. If you are studying acoustics, you should know it by now.

The subject is physics, not physic. Physic has another meaning.

i am not learning acoustics...but physics..sorry for the mis-spelling...i am sorry but i don't understand your approach

To find the time difference between a sound reaching your ear directly from the stage and the same sound reaching your ear after reflecting from the back wall, we need to consider the speed of sound and the distance traveled.

The sound travels at a speed of approximately 343 meters per second in air. Let's assume that the distance from the stage to your ear directly is D meters. Since you are seated in the middle row, the distance between the stage and your ear can be considered approximately half of the width of the auditorium, which is 29.0 meters.

First, we'll calculate the time taken for sound to reach your ear directly.

Time_direct = Distance_direct / Speed_of_sound

Time_direct = D / 343 m/s

Next, we'll calculate the time taken for sound to travel from the stage to the back wall and then back to your ear.

The total distance traveled by sound from the stage to the back wall and back is twice the distance from the stage to the back wall.

Distance_reflected = 2 * 29.0 m

Time_reflected = Distance_reflected / Speed_of_sound

Time_reflected = (2 * 29.0 m) / 343 m/s

Finally, we can find the time difference by subtracting the time taken directly from the time taken after reflection.

Time_difference = Time_reflected - Time_direct

Time_difference = [(2 * 29.0 m) / 343 m/s] - [D / 343 m/s]

This equation gives you the general time difference between the direct and reflected sound. However, to find the specific time difference experienced by the person seated in the middle row, you would need to substitute the actual distance D between the stage and your ear directly.