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Tension in harpsichord string

  1. Dec 5, 2006 #1
    A harpsichord string of length 1.60 m and linear mass density 25.0 mg/m vibrates at a (fundamental) frequency of 450 Hz.

    (a) What is the speed of the transverse string waves?
    I did 450 x 2(1.60) = 1440 m/s which is correct.

    (b) It asks for the tension.
    I tried it but am not getting the right answer.
    I used
    v = square root of (F / (m/L)) where v = 450 Hz, and m/L is 25000 kg/m
    So 1440 = squre root of (F/25000)
    F = 82.8 N which is incorrect.
    Not sure what I am doing wrong.

    Thanks
     
  2. jcsd
  3. Dec 6, 2006 #2

    OlderDan

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    450 Hz is a frequency, not a velocity, but it looks like you did in fact calculate the velocity correctly. 25mg/m is not 25000 kg/m
     
  4. Dec 6, 2006 #3
    Oops, I meant to say that v = 1440.
    So for this equation,
    v = square root of (F / (m/L))

    I know v and I am looking for F. But I am having trouble converting
    25 mg/m to m/L.
     
  5. Dec 6, 2006 #4

    OlderDan

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    1 mg = 1/1000 g
    1 g = 1/1000 kg

    All unit conversions involve multiplying by one. There are endless ways to write one, such as

    1 = 1000mg/g = 1g/1000mg
    1 = 1000g/kg = 1kg/1000g

    μ = 25mg/m*1*1*1*1*1*1*1*1*1*1*1 = 25mg/m
    μ = 25mg/m(1g/1000mg)(1kg/1000g) is still 25mg/m, but the units divide out to give

    μ = 25mg/m(1g/1000mg)(1kg/1000g) = .000025 kg/m
     
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