The assistant adjusts the tension in the same piano string, and a beat frequency

Question

The assistant adjusts the tension in the same piano string, and a beat frequency of 1.00 Hz is heard when the note and the tuning fork are struck at the same time.

(a) Find the two possible frequencies of the string.
flower =   437 Hz
fhigher =  439 Hz

(b) Assume the actual string frequency is the higher frequency. If the piano tuner runs away from the piano at 3.88 m/s while holding the vibrating tuning fork, what beat frequency does he hear?
f = Hz

(c) What beat frequency does the assistant on the bench hear? Use 343 m/s for the speed of sound.
f =   Hz

Also know that tuning fork has a frequency of 438Hz. Need anymore info?

Explanation / Answer

b) so now person will hear from the string

f = (v - vperson)/v f0 = (343-3.88)/343*439= 434 Hz

so fbeat = 438-434 = 4 Hz

c) so f heard by string when tuning fork ismoving = v/(v + vfork) f0

= 343/(343+3.88)*438= 433.1

so 439-433.1 = 5.9 Hz

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