Aclarinetist is playing the glissando at the beginning of Rhapsody in Blue, while Hermio...

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?