(Depth estimation through a two-layer water column)
(a) A lake has a warm surface layer 300m thick where the speed of sound is 1510m/s. Below this layer, the water is colder and the speed of sound is 1480m/s. A ship floating on the surface emits a pulse of ultrasound vertically downward and receives the echo from the lake bed after 0.92s. Treat the lake bed as a perfectly reflecting horizontal surface.
(b) (i) Write an expression for the total time taken by the pulse in terms of the unknown depth d of the lake bed below the interface of the two layers.
(c) (ii) Using the given numerical values, calculate the total depth of the lake below the ship.