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25 August, 20:46

Two-out-of-tune flutes play the same note. One produces a tone that has a frequency of 250 Hz, while the other produces 266 Hz. When a tuning fork is sounded together with the 250-Hz tone, a beat frequency of 9 Hz is produced. When the same tuning fork is sounded together with the 266-Hz tone, a beat frequency of 7 Hz is produced. What is the frequency of the tuning fork?

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  1. 25 August, 22:59
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    x = 259 Hz

    Explanation:

    given,

    frequency of one tuning fork = 250 Hz

    frequency of another tuning fork = 266 Hz

    when a tuning fork is sounded together beat frequency heard = 9

    let x be the frequency of unknown

    x - 250 = 9 Hz ... (1)

    x = 259 Hz

    when a another tuning fork is sounded together beat frequency heard = 7

    266 - x = 7 Hz ... (2)

    x = 259 Hz

    now, on solving both the equation the frequency comes out to be 259 Hz.

    so, The frequency of the tuning fork is equal to 259 Hz
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