Transverse Standing Waves?

A 37 cm length of wire has a mass of 6.0 g. It is stretched between two fixed supports and is under a tension of 160 N. What is the fundamental frequency of this wire?

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  • 1 decade ago
    Favorite Answer

    fundamental is L=(1/2) x wavelength

    L = 0.37 m so wavelength = 0.74

    V= square root tension of the string divided by the mass per unit length of the string which is = 99.331

    frequency = v/wavelength= 99.331/0.74=134.231 Hz

    the fundamental frequency is 134.231 Hz

  • Anonymous
    1 decade ago

    Hi

    Here's how to do it:

    You are going to use the wave equation v=fλ but first you need to ascertain λ and v.

    For a fixed wire, the fundamental mode has a node at each end and the longest wavelength that will satisfy this condition is λ=2L in other words you have 1/2 a wavelength on the wire.

    So we get λ=2*0.37=0.74m.

    Now the speed of the wave. The speed of the wave in a wire in v=√(T/μ) where 'T' is the tension in the wire and μ is the linear density (mass per unit length) of the wire.

    T=160N

    μ=0.006/0.37=0.0162 kg/m

    v=√(T/μ)=v=√(160/0.0162)=99.4m/s

    So now you know λ and v you can simply substitute into the wave equation v=fλ to find the fundamental frequency.

    v=fλ

    f=v/λ

    f=99.4/0.74=134Hz

  • 1 decade ago

    Is this your homework assignment?

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