Solving for Frequency of Tuning Fork: 1Hz & 3Hz Beats

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The problem involves two flutes producing frequencies of 262 Hz and 266 Hz, with a tuning fork creating beat frequencies of 1 Hz and 3 Hz when sounded with each flute. The beat frequency indicates that the tuning fork's frequency must be either 261 Hz or 263 Hz when paired with the 262 Hz flute, and either 263 Hz or 269 Hz with the 266 Hz flute. By combining these results, the only consistent frequency for the tuning fork is determined to be 263 Hz. This conclusion is reached through the understanding of beat frequencies as the difference between the tuning fork and flute frequencies. The final answer is that the frequency of the tuning fork is 263 Hz.
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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
 
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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
 

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