A person drops a rock down a 250-meter deep well. Upon impact with the bottom of the well a short burst of sound is produced with a frequency of 250 Hz. How long after he drops the rock does he...

A person drops a rock down a 250-meter deep well. Upon impact with the bottom of the well a short burst of sound is produced with a frequency of 250 Hz. How long after he drops the rock does he hear it hit the bottom of the well?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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A person drops a rock down a 250-meter deep well. Upon impact with the bottom of the well a short burst of sound is produced with a frequency of 250 Hz. Using this it has to be determined how long after the rock is dropped does the person hear it hit the bottom of the well.

To determine the time the value of the speed of sound is required and the acceleration due to gravitational force of the Earth is required.

Sound travels in air at 343.2 meters per second and the acceleration g = 9.8 m/s^2.

Assuming a time t taken for the rock to strike the bottom of the 250 m well, 250 = (1/2)*9.8*t^2

=> t = sqrt(51.02)

=> t = 7.14 s

The time taken by the sound made to travel up the well is 250/343.2 = 0.728 s

Adding the two, the person hears the rock hit the bottom 7.87 s after it is dropped.

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