How far (in m) is the surface of the snow from the device?

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.

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

(b) How deep (in m) is the snow?

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