A stationary microphone records the sound from a moving whistle. The digitally recorded data show the following frequency–time pairs for a 7 s interval:
• At t = –3 s, the frequency is 490 Hz.
• At t = 0 s, the frequency has risen linearly to 520 Hz.
• At t = +4 s, the frequency has fallen linearly to 470 Hz.
No other forces or motions are involved.
(a) Describe the motion of the whistle relative to the microphone during the 7 s interval, indicating the time periods during which the whistle is moving toward the microphone and moving away from it.
(b) Identify the instant of closest approach and justify your answer using the data.
(c) Compare the magnitude of the whistle’s speed during the approach phase with its speed during the receding phase, and explain the reasoning based on the slopes of the frequency–time data.
(d) State whether the rest frequency of the whistle is greater than, less than, or equal to any of the recorded frequencies, and justify your conclusion.