What is meant by "apparent frequency"? I mean the answer we get by applying the formula; what does it signify? If it is the frequency received by the observer, does it mean that the observer receives the same frequency no matter what the distance of the source? Shouldn't distance of play a role?
Actually, in an ideal situation distance of the source will not matter. In real life, the farther the source, the greater the damping effect on the wave. The sound loses energy and hence the amplitude and intensity fall.
However, this does not affect the frequency. Frequency is given by the formula fλ=v where symbols have usual meaning. When observer moves towards the sound source, he receives more waves per second, irrespective of the distance. When sound source moves towards observer distance between consecutive waves i.e wavelength decreases and hence frequency increases, depending only on speed of source and not distance. Everything related to frequency depends upon the speeds of the waves, source and observer.( I chose not to go in detail about the workings of the Doppler effect as that is not actually the focus of your question. I hope that you have a basic idea of this phenomenon).
Picture yourself at seaside, and consider the frequency at which waves are reaching your feet. This frequency does not depends on where you stand. Distance plays no role.
Now if you move towards the ocean, or towards the beach, the period between two successive waves is altered.
- If you run to the beach as fast as the wave moves, you will follow a crest and never get reached by the following one - the frequency is down to 0.
- If you run towards the ocean, you will face crest after crest more often then if you stay still - the frequency is increased.