How deep (in m) is the snow?

Question

A sonic depth gauge is placed 4.2 m above the ground. An ultrasound pulse sent downward reflects off snow and reaches the device 0.023 seconds after it was emitted. The air temperature is −20°C.

How far (in m) is the surface of the snow from the device? (Round your answer to at least three significant figures.)

How deep (in m) is the snow?

Answer 1

Sound travels more slowly through colder air. For temperatures reasonably close to 0 degrees celsius, the speed of sound through air can be calculated with the equation

Speed = 331.4 + 0.6 x (Temperature in Celsius) = 331.4 x 0.6(-20) = 319.4 m/s.

0.023 seconds is the "round trip" time for the sound pulse to travel to the top of the snow and return. Therefore, the time the pulse took to reach the snow was half that: 0.023/2 = 0.0115 s.

Now, we can use speed = distance/time to find how far the pulse travelled to the snow:

319.4 = distance/0.0115 -> distance = 319.4 x 0.0115 = 3.67 m. This is how far the device is from the surface of the snow.

The surface of the ground is 4.2 m away from the emitter, so the snow has a depth of 4.2 - 3.67 = 0.5 m.