Question

A flute player hears four beats per second when she compares her note to a 523 Hz tuning fork (the note C). She can match the frequency of the tuning fork by pulling out the ""tuning joint"" to lengthen her flute slightly. What was her initial frequency?

Answer 1

Answer:

527Hz

Explanation:

The beat frequency of any two waves is:

Fbeat =|f1 – f2|

i.e  

for frequency tied to length increase (wavelength increases as length increases, therefore frequency decrease::    Fbeat = f1+f2

for frequency tied to length decrease wavelength increases as length increases, therefore frequency also increases :    Fbeat = f1-f2

Note that a wavelength increase means a decrease of frequency because v = fλ

Therefore from the question:

Fbeat  =4 beats/s

F2 -523Hz

Fbeat = f1-f2

F1=Fbeat+F2

=523+4

=527Hz