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20 July, 13:07

A long string carries a wave; a 7.00-m segment of the string contains five complete wavelengths and has a mass of 180 g. The string vibrates sinusoidally with a frequency of 55.0 Hz and a peak-to-valley displacement of 20.0 cm. (The "peak-to-valley" distance is the vertical distance from the farthest positive position to the farthest negative position.) (a) Write the function that describes this wave traveling in the positive x direction. (Use the following as necessary: x and t. x is in meters and t is in seconds.) y =

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  1. 20 July, 14:26
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    y = 0.1sin (4.5x - 345.6t)

    Explanation:

    Parameters given:

    Length of 5 wavelengths = 7 m

    Length of one wavelength, λ = 7/5 = 1.4 m

    Frequency of wave, f = 55 Hz

    Peak to Valley displacement = 20 cm = 0.2 m

    Amplitude is half of the Peak to Valley displacement = 0.1 m

    The wave function of a wave traveling in the positive x direction is given generally as:

    y = Asin (kx - wt)

    Where A = amplitude

    k = Wave factor = 2π/λ

    x = displacement on the x axis

    w = angular frequency = 2πf

    t = time taken

    => Wave factor, k = 2π/λ = 2π / (1.4) = 4.5 m^ (-1)

    => Angular frequency, w = 2πf = 2π * 55 = 345.6 Hz

    Therefore, inserting all the necessary parameters, we get that the wave function is:

    y = 0.1sin (4.5x - 345.6t)
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