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?
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To calculate the time it takes for a sound to reach your ear directly and after reflecting from the back wall, we need to know the speed of sound in air. The speed of sound in air is approximately 343 meters per second at room temperature.
First, let's find the total distance the sound travels in both cases. When the sound reaches your ear directly, it travels a distance of 29.0 meters. When the sound from the stage reflects off the back wall and reaches your ear, it travels a total distance of twice the distance from the stage to the back wall because it has to travel to the back wall and back to your ear.
So the total distance traveled by the sound when it reflects off the back wall is 2 times 29.0 meters, which is 58.0 meters.
Now, we can find the time it takes for the sound to reach your ear directly and after reflecting from the back wall using the formula: time = distance / speed.
For the sound reaching your ear directly:
time_direct = 29.0 meters / 343 meters per second
For the sound reflecting from the back wall:
time_reflect = 58.0 meters / 343 meters per second
Calculating these values will give us the time it takes for the sound to reach your ear directly and after reflecting from the back wall.