How to solve this Physic question

Question

 A bat flying at 5.25 m/s is chasing an insect flying at 349 m/s in the same direction. The bat emits a steady chirpo of frequency 2000Hz

a. What frequency f0 does the insect hear
b. The insect becomes a moving source at frequency f0. What frequency does the bat hear reflected from the insect
c. The bat hears its own sound, plus the sound reflected by the insect. What beat frequency does the bat hear?

Answer 1

This is a good practice problem to understand waves, especially the Doppler effect and the interference effect beats. A few things to consider here:

1. It is always good to have an idea of what the answer will be, before you start doing calculations. This preliminary idea can help guide you toward the correct answer and can in many cases help you realize mistakes. In this case, will the frequencies the insect and the bat hear be higher or lower than the chirp frequency? The answer to this question comes from our understanding of how the waves are compressed or stretched out (for moving sources) or traversed more quickly or more slowly (moving observer).
2. Next, draw a figure of the problem so you can begin to form an idea of what is going on. Label everything that is given and sought for.
3. Now, there are some choices to be made when using the Doppler formula. The formula will take different shapes depending on what/who is moving and what/who is still. This choice is determined by the problem, but will vary between problems. The formula will also look different if it was light instead of sound, so be mindful of which formula you use! An additional complication with this problem is that both the bat and the insect are moving, because you cannot apply the Doppler formula directly.
4. The problem asks for three things and they are arranged in a logical, even chronological, order, This suggest that this is a good order to solve the problem in. In other cases, a different order might be more efficient.
5. Put everything together and work out the numbers.
6. Reread the question again and make sure you understood the problem correctly.
7. Check with your initial idea and modify as necessary.

I hope you find this helpful!