Aflute player hears four beats per second when she compares her note to a 523 hzhz 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.

527 Hz

Solution:

As per the question:

Beat frequency of the player,

Frequency of the tuning fork, f = 523 Hz

Now,

The initial frequency can be calculated as:

when

when

But we know that as the length of the flute increases the frequency decreases

Hence, the initial frequency must be 527 Hz

527 Hz

Explanation:

given,

flute beat = 4 beats/s

frequency of the tuning fork = 523 Hz

to find her initial frequency.

we know

  f₁ - f₂ = ±4

  f₁ = 523 ± 4 Hz

now,

f₁ = 527 Hz    (or)  519 Hz

when flute length increase the frequency decreases.

hence, initial frequency is equal to 527 Hz