I have a-e answered, however I can not get f to work. A sinusoidal transverse wa

Question

I have a-e answered, however I can not get f to work. A sinusoidal transverse wave is traveling along a string in the negative direction of an x axis. The figure below shows a plot of the displacement as a function of position at time t = 0. The x axis is marked in increments of 25 cm and the y axis is marked in increments of 2.5 cm. The string tension is 4.9 N, and its linear density is 26 g/m. (a) Find the amplitude. m (b) Find the wavelength. m (c) Find the wave speed. m/s (d) Find the period of the wave. s (e) Find the maximum speed of a particle in the string. m/s (f) Complete the equation describing the traveling wave, in which x and y are in meters and t is in seconds. y(x, t) = sin( x + t + )

Explanation / Answer

a. Amplitude = maximum displacment from zero = 5.0 cm b. Wavelength ? = distance beteen two consequrive crests (or troughs) = 40 cm c. wave speed v = v(Tension / linear density) = v(T/µ) µ = 24 g/m = 2.40 * 10-2 kg/m v = v(4.4 / 2.40 * 10-2) = 13.54 m/s d. Period T = ?/v = 0.40 m / 13.54 = 2.95 * 10-2 s e. Maximum transverse speed vt = ? * A = (2 * p / T) * A = 2 * 3.14 * 0.05 / 2.95 * 10-2 = 10.64 m/s f. wave no. k = 1/? = 1/0.40 = 2.5 m-1 g. angular frequency ? = 2p/T = 6.28 / 2.95 * 10-2 = 2.13 * 102 rad/s h. y = ym * sin (kx - ?t + f) at t = 0, y = 4.0 cm = 0.04 m ym = A = 0.05 m, x = 0 => 0.04 = 0.05 * sin ( k * 0 - ? * 0 + f) sin f = 4/5 f = sin-1 (0.80) = 53.130

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