What is the magnitude of the detected sound frequency shift from 170 hz during the projectile flight described in the passage?

The magnitude of the frequency shift (that is the change in frequency) first falls to zero, then increases. This is so because as the projectile moves upward, the position of the sound source is constantly changing and as a result there would be a difference between the frequency of the sound emitted and the sound received by the microphone (that is the frequency shift). A point will be reached in the projectile's motion when the projectile will be momentarily at rest. (At the highest point reached in its flight h).

Explanation:

At this point, the frequency emitted by the source becomes equal to that received by the microphone. This can be seen from the equation 2 for Doppler effect contained in the attachment below.

This moment is short lives and the projectile soon starts a return journey downward under the influence of gravity. The velocity of the projectile is negative ( v < 0 ) and from the equation can be confirmed that the frequency received by the microphone increases as the projectile fall under gravity. This is so because as the projectile falls downward it velocity becomes more and more negative. And from the equivalent in the picture below, the frequency received by the microphone increases

Thank you very much and I hope this was helpful.

they start with the same