A sinusoidal transverse wave is traveling along a string in the negative directi

Question

A sinusoidal transverse wave is traveling along a string in the negative direction of a 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 10 cm and the y axis is marked in increments of 2.5 cm. The string tension is 3.1 N, and its linear density is 2.9 g/m. Include rad in your units where needed. Find the amplitude. Find the wavelength. Find the wave speed. Find the period of the wave. Find the maximum transverse speed of a particle in the string. Find the phase angle Complete the equation describing the traveling wave, in which x and y are in meters and t is in seconds. y(x, t) = m) sin[(rad/m)x + (rad/s)t + (rad)]

Explanation / Answer

(A) A = Ymax = 5 Y = 5 x 10 cm = 50 cm

(B) lambda = 4 X = 4 x 2.5 = 10 cm

(c) v = sqrt [ T / mu ]

= sqrt[ 3.1 / (29 x 10^-3 kg/m)] = 10.34 m/s

(d) T = lambda / v = 0.10 m / 10.34 = 9.67 x 10^-3 sec

(e) w = 2 pi / T = 649.68 rad/s

Vmax = A w = 0.50 x 649.68 = 324.84 m/s

(f) k = 2pi / lambda = 62.8 rad/m

y = 0.50 m sin[ (62.8 x ) + ( 649.68 t) + phi]

at t = 0 and x = 0

y = 40 cm = 0.40 m

0.40 = 0.50 sin(phi)

phi =0.93 rad

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y = 0.50 m sin[ (62.8 x ) - ( 649.68 t) + 0.93]

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