Consider a sound wave modeled with the equation s(x, t) = 3.00 nm cos(3.50 m−1x − 1,800 s−1t). What is the maximum displacement (in nm), the

Question

Consider a sound wave modeled with the equation s(x, t) = 3.00 nm cos(3.50 m−1x − 1,800 s−1t). What is the maximum displacement (in nm), the wavelength (in m), the frequency (in Hz), and the speed (in m/s) of the sound wave?

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Ngọc Hoa 3 years 2021-08-18T20:36:20+00:00 1 Answers 27 views 0

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  1. Acacia
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    2021-08-18T20:38:00+00:00
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    Answer:

    –   maximum displacement = 3.00nm

    –   λ = 1.79m

    –  f = 286.47 s^-1

    Explanation:

    You have the following equation for a sound wave:

    s(x,t)=3.00nm\ cos(3.50m^{-1}x- 1,800s^{-1} t)              (1)

    The general form of the equation of a sound wave can be expressed as the following formula:

    s(x,t)=Acos(kx-\omega t)            (2)

    A: amplitude of the wave = 3.00nm

    k: wave number = 3.50m^-1

    w: angular frequency = 1,800s^-1

    – The maximum displacement of the wave is given by the amplitude of the wave, then you have:

    maximum displacement = A = 3.00nm

    – The wavelength is given by :

    \lambda=\frac{2\pi}{k}=\frac{2\pi}{3.50m^{-1}}=1.79m

    The values for the wavelength is 1.79m

    – The frequency is:

    f=\frac{\omega}{2\pi}=\frac{1,800s^{-1}}{2\pi}=286.47s^{-1}

    The frequency is 286.47s-1

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