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10 August, 08:20

The lowest musical note on a grand piano has a string frequency of 27.5 Hz. The entire string is 2.00 m long and has a mass of 400. g. The vibrating section of the string is 1.90 m long. What tension force is needed to tune this string properly?

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  1. 10 August, 10:37
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    The tension force needed to tune the string properly is 2184.05 N

    Explanation:

    Frequency is inversely proportional to the length l of the wire and directly proportional to the square root of the tension and it can be shown that the frequency of vibration is given by.

    f = (1/2*l) (T/m) ^ (0.5)

    Where, T = tension in the string

    f = frequency = 27.5 Hz

    l = length = 1.9 m

    m = mass per unit length

    Total string length = 2 m

    Mass of string = 400 g

    Unit mass = 400 g/2 m = 200 g / m

    Therefore

    27.5 Hz = 1 / (2*1.9) * (T/0.2) ^ (0.5)

    Therefore, T = 2184.05 N

    The required tension is 2184.05 N
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