A transverse periodic wave is established on a string. The wave is described by the expression y = 0.005 sin(20.0x + 2ft) where y is in met

Question

A transverse periodic wave is established on a string. The wave is described by the expression y = 0.005 sin(20.0x + 2ft) where y is in meters when x and t are in meters and seconds, respectively. If the wave travels with a speed of 20.0 m/s, what is its frequency, f?

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Adela 4 years 2021-08-11T23:54:50+00:00 1 Answers 40 views 0

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  1. trucchi
    0
    2021-08-11T23:56:48+00:00
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    Answer:

    f =63.64Hz

    Explanation:

    The equation of the transverse periodic wave

    y = 0.005 sin(20.0x + 2ft)

    From the equation we can deduce that

    Amplitude A = 0.005

    Wave number K = 20

    Angular frequency w = 2πf

    We are asked to find the frequency (f)

    the formular for the wave number is given as K = 2π / lambda

    Lambda = 2π/ K

    Lamda is the wavelength

    = 2 × 3.142 /20

    = 0.3142m

    The velocity of the wave is expressed as v = frequency × lamba (wavelength)

    Frequency = velocity / wavelength

    f = 20/ 0.3142

    f = 63.65Hz

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