Two out-of-tune flutes play the same note. one produces a tone that has a frequency of 249 hz, while the other produces 285 hz. when a tuning fork is sounded together with the 249-hz tone, a beat frequency of 19.0 hz is produced. when the same tuning fork is sounded together with the 285-hz tone, a beat frequency of 17.0 hz is produced. what is the frequency of the tuning fork?

268 Hz

Explanation:

given,

frequency produced by the first flute = 249 Hz

frequency from another flute = 285 Hz

beat frequency produced  with 249 Hz tone= 19 Hz

beat frequency produced  with 285 Hz tone= 17 Hz

frequency of the tuning fork = ?

Let the frequency of the fork will be equal to x Hz

now,

x - 249 = 19 Hz(1)

285 - x = 17 Hz(2)

on solving both the equation

from equation (1)

x = 19 + 249

x = 268 Hz

from equation (2)

285 - x = 17 Hz

x = 285-17

x = 268 Hz

So, the frequency of the tuning fork is equal to  268 Hz