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Dee asked in Science & MathematicsPhysics · 1 year ago

The transverse displacement (y) of a wave is given as a function of position...?

Consider the waveform expression. 

 Y (x,t) = ymSin(1.73 + 0.435x +531t)

The transverse displacement (y) of a wave is given as a function of position (x in meters) and time (t in seconds) by the expression. Determine the wavelength, frequency, period, and phase constant of this waveform.

λ = ? Metres 

T= ? Seconds 

f = ? Hertz 

ϕ = ? Radians

1 Answer

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  • 1 year ago
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    I'll note that I'm more of a math person than a physics person, but I'm trying to get up to speed on wave equations (hence no guarantees). Here's what I got after reviewing transverse waves.

    transverse wave equation:

    y(x, t) = A sin(kx ∓ ωt + 𝜙)

    amplitude: A

    wave number: k = 2π/λ

    angular frequency: ω = 2π/T

    velocity: v = ω/k

    phase shift: 𝜙

    wavelength: λ = 2π/k

    period: T = 2π/ω

    frequency: f =1/T

    ----

    Y(x,t) = ym sin(1.73 + 0.435x + 531t)

    Comparing the transverse wave equation to the expression in the question,

    k = 0.435 m⁻¹

    ω = 531 s⁻¹

    𝜙 = 1.73 radians

    so

    wavelength: λ = 2π/k = (2π / 0.435 m⁻¹) = 14.4 m

    period: T = 2π/ω = (2π / 531 s⁻¹) = 0.0118 s

    frequency: f = 1/T = (1 / 0.0118 s) = 84.7 s⁻¹

    phase constant: 𝜙 = 1.73 radians

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