Finding tuning fork frequency from beat frequencies

[physicsdawg]

Homework Statement

Two out-of tune flutes play the same note. One produces a tone that has a frequency of 262 Hz, while the other produces 266 Hz. When a tuning fork is sounded together with the 262-Hz tone, a beat frequency of 1 Hz is produced. When the same tuning fork is sounded together with the 266 Hz tone, a beat frequency of 3 Hz is produced. What is the frequency of the tuning fork?

Homework Equations

The Attempt at a Solution

kind of lost, originally tried

266-262= 4 and tried setting up a proportion of 262/1=266/3x or something but got nowhere. thanks to anyone who can help solvethis

 

[vipulsilwal]

answer is 263 Hz.
beats = difference in frequencies (it is just a formula , but its significance it more than jst its simple formula)..

from 1st part of question [[When a tuning fork is sounded together with the 262-Hz tone, a beat frequency of 1 Hz is produced]]
the frequency can either be 261 or 263 hz

from 2nd part of question [[When the same tuning fork is sounded together with the 266 Hz tone, a beat frequency of 3 Hz is produced]]
frequency can be 263 or 269 Hz

combine both results we get 263 Hz