Question

The back wall of an auditorium is 23.0 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? The speed of sound in the air is 343 m/s .

_________seconds

Answer 1

0.067 seconds

Step-by-step explanation:

The time needed for a person seated in the middle row to receive a sound from the stage, can be calculated assuming that the sound is moving in a straight line at constant speed, taking into account that the distance traveled will be half of the distance between the stage and the back wall:

t₁ = x₁ / v = 11.5 m / 343 m/s = 0.034 sec

The same sound, after reflecting from the back wall, will travel a distance equal to one and a half the distance between the stage and the back wall:

t₂ = 34.5 m /343 m/s = 0.101 sec

The time elapsed between both sounds will be equal to the difference between t₂ and t₁, as follows:

t₂ - t₁ = 0.101 sec - 0.034 sec = 0.067 sec.