The equation of a wave is represented by: Y = 0.005sin 2π(0.5x – 200t) where x and y are in meters and t in seconds. Find its i. Amplitude

Question

The equation of a wave is represented by: Y = 0.005sin 2π(0.5x – 200t) where x and y are in meters and t in seconds. Find its i. Amplitude ii. Angular speed iii. Frequency iv. Period v. Wave number vi. Wavelength vii. speed.

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Hưng Khoa 6 months 2021-08-15T15:31:34+00:00 1 Answers 0 views 0

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    2021-08-15T15:33:31+00:00

    Answer:

    See solution below

    Explanation:

    The standard equation of a wave is represented by: Y = Asin 2π(x/λ – ft)

    A is the amplitude

    λ is the wavelength

    f is the frequency

    t is the time

    Comparing the standard with the given equation Y = 0.005sin 2π(0.5x – 200t)

    i) A = 0.005m

    Amplitude is 0.005m

    ii) ω = 2πf

    ω = 2π(200)

    ω = 400π rad/s

    iii) ω = 2πf

    400π = 2πf

    200 = f

    Swap

    f = 200Hertz

    iv) Period = 1/f

    Period = 1/200

    Period = 0.005secs

    v) wave number  =

    vi) Wavelength λ

    0.5x = x/λ

    0.5 = 1/λ

    λ  = 1/0.5

    λ = 2m

    vii) velocity – fλ

    velocity = 200 * 2

    velocity = 400m/s

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