Question

Question 1: At a height of ten meters above the surface of a freshwater lake, a sound pulse is generated. The echo from the bottom of the lake returns to the point of origin 0.175 s later. The air and water temperatures are 20 ^oC. How deep is the lake?

Question2: A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another. He is closer to one cliff than the other. He fires a gun and, after a while, hears three echoes. The second echo arrives 1.92 s after the first, and the third echo arrives 1.46 s after the second. Assuming that the speed of sound is 343 m/s and that there are no reflections of sound from the ground, find the distance (in m) between the cliffs.

Answer 1

1)

The sound pulse travels twice the distance in air( ) ( height above surface of water) and twice the distance from surface of water to bottom of lake to produce an echo.

Total time taken for the echo is

Velocity of sound in air

Velocity of sound in fresh water

Height above surface of water where sound pulse is produced is

Time taken for the echo is

Depth of lake is

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2)

Distance of hunter from nearby wall is

Distance of hunter from faroff wall is

The first echo (from the nearby wall) travels a distance , time taken by first echo to reach hunter is ( v is velocity of sound)

The second echo (from the faroff wall) travels a distance , time taken by second echo to reach hunter is

The third echo ( second echo reflected by nearby wall ) travels a distance , time taken by third echo is  

​Given that   

Total distance between the cliffs is