A stretched string has a mass per unit length of 4.87 g/cm and a tension of 16.7 N. A sinusoidal wave on this string has an amplitude of 0.1

Question

A stretched string has a mass per unit length of 4.87 g/cm and a tension of 16.7 N. A sinusoidal wave on this string has an amplitude of 0.101 mm and a frequency of 71.0 Hz and is traveling in the negative direction of an x axis. If the wave equation is of the form y(x,t) = y_m sin(kx + ωt), what are (a) y_m, (b) k, and (c) ω, and (d) the correct choice of sign in front of ω?

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Thu Cúc 22 mins 2021-07-22T09:52:25+00:00 1 Answers 0 views 0

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    2021-07-22T09:54:15+00:00

    Answer:

    Explanation:

    Given that,

    Mass per unit length is

    μ = 4.87g/cm

    μ=4.87g/cm × 1kg/1000g × 100cm/m

    μ = 0.487kg/m

    Tension

    τ = 16.7N

    Amplitude

    A = 0.101mm

    Frequency

    f = 71 Hz

    The wave is traveling in the negative direction

    Given the wave form

    y(x,t) = ym• Sin(kx + ωt)

    A. Find ym?

    ym is the amplitude of the waveform and it is given as

    ym = A = 0.101mm

    ym = 0.101mm

    B. Find k?

    k is the wavenumber and it can be determined using

    k = 2π / λ

    Then, we need to calculate the wavelength λ using

    V = fλ

    Then, λ = V/f

    We have the frequency but we don’t have the velocity, then we need to calculate the velocity using

    v = √(τ/μ)

    v = √(16.7/0.487)

    v = 34.29

    v = 5.86 m/s

    Then, we can know the wavelength

    λ = V/f = 5.86 / 71

    λ = 0.0825 m

    So, we can know the wavenumber

    k = 2π/λ

    k = 2π / 0.0825

    k = 76.18 rad/m

    C. Find ω?

    This is the angular frequency and it can be determined using

    ω = 2πf

    ω = 2π × 71

    ω = +446.11 rad/s

    D. The angular frequency is positive (+) because the direction of propagation of wave is in the negative direction of x

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