When dolphin swims close to its prey, it transmits sound waves to figure out details (like direction where the fish is moving) of its prey. Now, if the frequency of the reflected waves has increased, would the dolphin catch up its prey or fall behind? Explain your answer.

The frequency of the waves depends on the distance between wave fronts - considering a front as a maximum disturbance of the wave

(Consider the waves emitted by an organ pipe: condensation and rarefactions)

The waves themselves are a fixed distance apart -

as one moves towards the source the waves received will be closer together (higher frequency)

So if the frequency received increases, the distance between the source and the observer must be decreasing

newton's first law of motion

this is a good question! i'll do some research and come back when i have the answer!