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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?

Respuesta :

Answer:

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

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