For a particular transverse wave that travels along a string that lies on the x-

Question

For a particular transverse wave that travels along a string that lies on the x-axis, the equation of motion is: y (0.0350 m) cos (45.0 rad/s)t - (0.500 m1)x (a) Determine the wave's amplitude, wavelength, and frequency. amplitude wavelength frequency Hz (b) Calculate the speed of the wave. m/s (c) Calculate the tension in the string, if the string has a mass per unit length of 0.0400 kg/m. (d) In which direction is the wave traveling? in the negative x-directiorn in the positive x-direction neither: the wave is a standing wave (e) Calculate the maximum transverse speed of a point on the string. m/s (f) Calculate the displacement (in other words, the y-value) of a point at x = 1.00 m when t = 6.00 s.

Explanation / Answer

(A) amplitude = 0.0350 m

wavelength = 2 pi / k = 2 pi / 0.5 = 12.6 m

frequency = w / 2pi = 7.2 Hz

(b) v = w / k = 45 / 0.5 = 90 m/s

(C) u = 0.040 kg / m

v = sqrt[ T / u ]

T = 324 N

(d) in the +ve x direction

(e) v_max = A q = 0.0350 x 45 = 1.575 m/s

(f) y = 0.0350 cos[ (45 x 6) - (0.5 x 1)]

y = - 0.033 m

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