When a guitar string is sounded with a 440 Hz tuning fork, a beat frequency of 5 Hz is heard. Let the experiment be repeated with a tuning fork of 437 Hz. Then, the beat frequency is found to be 8 Hz. What is the string frequency (in Hz)?

Let, Frequency of string = f difference in frequency gives us number of beats produced per second,

case - (1)

Beat produced with first tuning fork

$|f-440|=5\dots \text{ (i) }$

possible value of f  = 445, 435

case - (2)

Beat produced with second tuning for

$|\mathrm{f}-437|=8$…… (ii)

possible value of f = 445, 429

considering both cases, we get

f = 445 Hz