The wave function for a traveling wave on a taut string is (in SI units) y(x,t)

ID: 1864897 • Letter: T

Question

The wave function for a traveling wave on a taut string is (in SI units) y(x,t) = 0.315 sin 15?t ? 1?x + ? 4

(a) What are the speed and direction of travel of the wave? speed __________ m/s __________ direction

(b) What is the vertical position of an element of the string at t = 0, x = 0.147 m? __________ m

(d) What is the frequency of the wave? __________ Hz

(e) What is the maximum transverse speed of an element of the string? __________ m/s

y(x,t)-0.315 sin( 15nt-imx + 4)

from the given equation

w = 15*pi = 47.1 rad/s

k = pi = 3.14 m^-1

a) wave is propagating along the positive x axis

wave speed v = w/k = 15pi/pi = 15 m/s

b) y = 0.315sin(-3.14*0.147+pi/4)

y = 0.1001 m

c) wavelength = lambda = 2pi/k = 2pi/pi = 2 m

d) frequency f = w/2pi = 15pi/2pi = 7.5 Jz

e) v max = Aw = 0.315*47.1 = 14.84 m/s

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