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 an x axis. The figure shows a snapshot of the displacement as a function of position at time 1= 0; the scale of the y axis is set by y_s = 4.0 cm. The string tension is 3.6 N, and its linear density is 25 g/m. Find the (a) amplitude, (b) wavelength, (c) wave speed, and (d) period of the wave, (e) Find the maximum transverse speed of a particle in the string. If the wave is of the form y(x, t) = y_msin(kx + or - omega t + phi), what are (f) k, (g) omega , (h) phi, and (i) the correct choice of sign in front of omega NOTE this problem uses "SIN" instead of "COS"

Explanation / Answer

a)

maximum vertical displacement

amplitude = A = 5 cm

b)

distance between point of same phase (same height on graph)

wavelength = 40 cm

c)

wave speed = sqrt(T/u) = sqrt(3.6/0.025) = 12 m/s

d)

T = wavelength/v = 0.4/12 = 0.033 s

e)

vmax = A*w = A*2pi/T = 0.05*2*pi*12/0.4 = 9.4 m/s

f)

k = 2pi/wavelength = 2pi/0.4 = 16 /m

g)

w = v/k = 190 = 1.9*10^2 rad/s

h)

at t = 0 , x = 0 ,,y = 4 cm

4 = 5*sin(phi)

phi = 0.93 rad

i)

for a wave in -x direction

y = ym*sin(kx+wt+phi)

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