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17 April, 04:09

Two violinists are playing their "A" strings. Each is perfectly tuned at 440 Hz and under 245 N of tension. If one violinist turns her peg to tighten her A string to 251 N of tension, what beat frequency will result

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  1. 17 April, 04:30
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    450.78Hz

    Explanation:

    The frequency of wave in string is directly proportional to its tension. This is mathematically expressed as

    F∝T

    F = kT where k is the constant of proportionality

    From the formula, k = F/T

    F1/T1 = F2/T2 = k

    If each violin is perfectly tuned at 440 Hz and under 245 N of tension then F1 = 440Hz, T1 = 245N

    To get the frequency if the string A is tighten to 251N of tension,

    T2 = 251N, F2 = ?

    Substituting the given values into the equation above to get F2 we have;

    440/245 = F2/251

    Cross multiplying

    245F2 = 440*251

    245F2 = 110,440

    F2 = 110,440/245

    F2 = 450.78Hz
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