2. Biologists think that some spiders “tune” strands of their web to give enhanced response at frequencies corresponding to those at which d

Question

2. Biologists think that some spiders “tune” strands of their web to give enhanced response at frequencies corresponding to those at which desirable prey might struggle. Orb spider web silk has a typical diameter of 20 μm, and spider silk has a density of 1300 kg/m3. To have a fundamental frequency at 100 Hz, to what tension must a spider adjust a 12-cm-long strand of silk?

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Bình An 5 years 2021-07-18T17:23:26+00:00 2 Answers 289 views 0

Answers ( )

  1. ngockhue
    0
    2021-07-18T17:25:16+00:00
    Reply

    Answer: 2.35*10^-4 N

    Explanation:

    The linear mass density is

    μ = m / L

    Recall, ρ = m / V, so that, m = ρV

    Substitute this in the equation

    μ = ρV / L

    Also, recall, V = AL. Substituting this in the equation, we have

    μ = ρAL / L = ρA

    Again, recall, A = πr², so that

    μ = ρπr²

    μ = 1300 * 3.142 * [10*10^-6]²

    μ = 4.085*10^-7 kg/m

    the wavelength of the wave in the silk, λ = 2L

    λ = 2 * 0.12 = 0.24 m

    The wave speed, v = fλ

    v = 100 * 0.24 = 24 m/s

    v = √(T / μ)

    v² = T / μ

    T = v²μ

    T = 24² * 4.085*10^-7

    T = 2.35*10^-4 N

  2. thienhuong
    0
    2021-07-18T17:25:22+00:00
    Reply

    Answer:

    The tension is 2.35×10⁻⁴N

    Explanation:

    Given:

    d = 20 μm = 20×10⁻⁶ m

    L = 12 cm = 0.12 m

    f = 100 Hz

    The transverse velocity is:

    v=\sqrt{\frac{T_{s} }{\mu } } (eq. 1)

    Where

    Ts = web´s tension

    μ = linear mass density

    The linear mass density is:

    \mu =\frac{\pi d^{2}\rho }{4} (eq. 2)

    Where

    ρ = density of the spider silk = 1300 kg/m³

    The fundamental frequency is:

    f=\frac{v}{2L}

    Replacing eq. 1 and 2 and clearing the tension Ts:

    f=\frac{1}{2L} \sqrt{\frac{4T_{s} }{\pi d^{2}\rho } } \\T_{s} =\pi d^{2} f^{2} L^{2} \rho

    T_{s} =\pi *(20x10^{-6} )^{2}*(100 )^{2} *(0.12 )^{2}*1300=2.35x10^{-4} N

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