Two-out-of-tune flutes play the same note. One produces a tone that has a frequency of 250 Hz, while the other produces 266 Hz. When a tuning fork is sounded together with the 250-Hz tone, a beat frequency of 9 Hz is produced. When the same tuning fork is sounded together with the 266-Hz tone, a beat frequency of 7 Hz is produced. What is the frequency of the tuning fork?

x = 259 Hz

Explanation:

given,

frequency of one tuning fork = 250 Hz

frequency of another tuning fork = 266 Hz

when a tuning fork is sounded together beat frequency heard = 9

let x be the frequency of unknown

x - 250 = 9 Hz ... (1)

x = 259 Hz

when a another tuning fork is sounded together beat frequency heard = 7

266 - x = 7 Hz ... (2)

x = 259 Hz

now, on solving both the equation the frequency comes out to be 259 Hz.

so, The frequency of the tuning fork is equal to 259 Hz