Aclarinetist is playing the glissando at the beginning of Rhapsody in Blue, while Hermione (who arrived late) is walking toward her seat. If the (changing) frequency of the note is f and Hermione is moving toward the clarinetist at speed v, then she actually hears the frequency φ given by
where c is the (constant) speed of sound in air, about 330 m/sec. At this particular moment, the frequency is f = 440 Hz and is increasing at a rate of 100 Hz per second. At that same moment, Hermione is moving toward the clarinetist at 4 m/sec and decelerating at 2 m/sec2. What is the perceived frequency φ she hears at that moment? How fast is it changing? Does Hermione hear the clarinet’s note becoming higher or lower?
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