physics question

Question

A sonic depth gauge is placed 4.4 m above the ground. An ultrasound pulse sent downward reflects off snow and reaches the device 0.024 seconds after it was emitted. The air temperature is −20°C.

(a)

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

  m

(b)

How deep (in m) is the snow?

 m

Answer 1

I can explain this question with proper diagram

Speed of sound at -20degree C = 320 m/s ( air)

Speed of sound at 0degree C = 332 m/s ( snow)

Wave travels 2(4.2-d) in air in time t1

and 2d in snow in snow in time t2

t1 = 2(4.2-d)/320 and t2 = 2d/332

t1+t2 = 0.023 sec

0.023 = 2(4.2-d)/320 + 2d /332

Find d

d= Thickness of snow (in m)

4.2 -d = distance of upper surface of snow from device

you get both answers