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Posted by on Thursday, August 16, 2012 at 1:34am.

a wire under tension vibrates with a fundamental frequency of 256Hz. what would be the fundamental frequency if the wire were half as long, twice as thick, and under 1/4 tension?

  • physics - , Thursday, August 16, 2012 at 3:36am

    The speed of transverse waves is the squareroot of (T/p), where p is the density per unit length, and T is the tension foorce. The density per unit length is 4x higher for the shorter, fatter wire, and T is 1/4 as high, to the sound speed is 1/4 as large.

    The wavelength of the fundamental is 1/2 as long due to the shorter length.

    The fundamental frequency scales with (sound speed)/(wavelength), and gets multiplied by (1/4)/(1/2) = 1/2

  • Physics - , Sunday, November 1, 2015 at 3:57am

    f1=v1/L1=(1/L1)(T1/μ1)^1/2
    f2=v2/L2=(1/L2)(T2/μ2)^1/2
    then
    f2/f1=(L1/L2)[T2μ1/(T1μ2)]^1/2
    where
    L2=1/2L1
    T2=1/4T1
    μ2=ρS2=4ρS1=4μ1
    then
    f2=1/2f1
    f2=128 hz

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