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Frequency, transverse waves, low-pitch strings

  1. Nov 5, 2014 #1

    rlc

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    1. The problem statement, all variables and given/known data
    Two identical guitar strings are stretched with the same tension between supports that are not the same distance apart. The fundamental frequency of the higher-pitched string is 380Hz, and the speed of transverse waves in both wires is 200 m/s. How much longer is the lower-pitched string if the beat frequency is 4Hz?

    2. Relevant equations
    None have worked!

    3. The attempt at a solution
    Every yahoo answers solution has not worked for me. Please help!
     
  2. jcsd
  3. Nov 5, 2014 #2

    BvU

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    None meaning which ones ?

    Have you attempted a solution ? If so, show your work. Every one of them that didn't work according to you. There must be a way out of this; perhaps one of the dead ends still has an opening somewhere ...
     
  4. Nov 5, 2014 #3

    rlc

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    y=y0[sin(2pif1t)+sin(2pif2t)]

    Is this the right equation to use?
     
  5. Nov 5, 2014 #4

    BvU

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    you need something to connect tension, lenght and frequency. an equation where some or all appear.

    If the beat frequency is 4 Hz, how much is the frequency of the lower-pitched string ?
     
  6. Nov 5, 2014 #5

    rlc

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    f = (1/2L)*√(T/μ)
    where
    • f is the frequency in hertz (Hz) or cycles per second
    • T is the string tension in gm-cm/s²
    • L is the length of the string in centimeters (cm)
    • μ is the linear density or mass per unit length of the string in gm/cm
    • √(T/μ) is the square root of T divided by μ in seconds
    The transverse wave speed v in a flexible string or wife is given by:
    v=SQRT(T/u)
    where T is tension and u is the mass per unit length of the string

    Beats are the difference between two frequencies: ABSOLUTE VALUE OF (f1-f2)
     
  7. Nov 5, 2014 #6

    rlc

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    I got it!
    f=(1/2L)(transverse wave speed)
    380=(1/2L)(200)
    L=0.263157 m

    Beat frequency=f1-f2
    380-4=376 (I know that you can add or subtract the 4, but I went with subtracting first just to try)
    376=(1/2L)(200)
    L=0.265957

    Subtract the two L's:
    0.265957-0.263157=2.80E-3 m (which the online homework program says is the right answer)
     
  8. Nov 6, 2014 #7

    BvU

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    It wasn't a matter of trial and error: they were specifically asking for the lower-pitched string.
    Other than that: good work!
    It shows how difficult playing string instruments really is: just a fraction away from the right position and you get undesired beats.
     
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