The frequency of vibration of a piano string varies directly as the square root of the tension on the string and inversely as the length of

Question

The frequency of vibration of a piano string varies directly as the square root of the tension on the string and inversely as the length of the string. The middle A string has a frequency of 440 vibrations per second. Find the frequency of a string that has 1.25 times as much tesnsion and is 1.2 times as long.

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Melanie 1 week 2021-10-09T19:44:33+00:00 1 Answer 0

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    2021-10-09T19:45:57+00:00

    Answer:

      about 409.946 Hz

    Step-by-step explanation:

    The multiplier of frequency is (√(tension multiplier))/(length multiplier), so is …

      (√1.25)/1.2 = (5/12)√5 ≈ 0.931695

    So, the longer, tighter string will have the lower frequency of about …

      0.931695×440 Hz ≈ 409.946 Hz

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