A research vessel floats above a region of the ocean that is covered by a warm surface layer and a colder deep layer.
The warm layer is 300m thick and the speed of sound in this layer is 1530m/s. In the colder deep water the speed of sound is 1500m/s.
The vessel emits a short ultrasonic pulse straight downward. The total time between emission of the pulse and reception of its echo from the seabed is measured to be 2.40s.
Answer the following questions on the basis of these data.
(i) Explain, with suitable reasoning, why the pulse passes through the warm layer twice during its journey.
(ii) If t1 is the total time spent by the pulse inside the warm layer, express t1 in terms of the known quantities and the unknown depth H of the seabed below the vessel.
(iii) Derive an equation relating the total travel time 2.40s, the given speeds, the thickness of the warm layer and the depth H.
(iv) Calculate the numerical value of H.