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Two out-of-tune flutes play the same note. One produces a tone that has a frequency of 246 Hz, while the other produces 289 Hz. When a tuning fork is sounded together with the 246-Hz tone, a beat frequency of 18.0 Hz is produced. When the same tuning fork is sounded together with the 289-Hz tone, a beat frequency of 25.0 Hz is produced. What is the frequency of the tuning fork

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Answer:

[tex]264\ \text{Hz}[/tex]

Explanation:

Beat frequency of the first case = 18 Hz

Beat frequency of the second case = 25 Hz

Tone of first fork = 246 Hz

Tone of second fork = 289 Hz

First case

Beat frequency is given by

[tex]\Delta f=|f_2-f_1|\\\Rightarrow f_1=246\pm18\\\Rightarrow f_1=264, 228\ \text{Hz}[/tex]

Second case

[tex]f_2=289\pm 25\\\Rightarrow f_2=264, 314\ \text{Hz}[/tex]

The frequency of the tuning fork is [tex]264\ \text{Hz}[/tex].

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