The wave function for a traveling wave on a taut string is (in SIunits) the foll

Question

The wave function for a traveling wave on a taut string is (in SIunits) the following equation. y(x, t) = (0.382 m)sin(14t - 3x + /4) (a) What are the speed and direction of travelof the wave?
1 m/s

(b) What is the vertical position of an element of the string att = 0, x = 0.172m?
3 m

(c) What is the wavelength of the wave?
4 m
What is the frequency of the wave?
5 Hz

(d) What is the maximum magnitude of the transverse speed of thestring?
6 m/s y(x, t) = (0.382 m)sin(14t - 3x + /4) (a) What are the speed and direction of travelof the wave?
1 m/s

(b) What is the vertical position of an element of the string att = 0, x = 0.172m?
3 m

(c) What is the wavelength of the wave?
4 m
What is the frequency of the wave?
5 Hz

(d) What is the maximum magnitude of the transverse speed of thestring?
6 m/s

Explanation / Answer

(a)   speed = / k = 14 /3   = 4.6667 m/s    inthe + x direction . (b)   vertical position... use the given equation tocalc y: .    y = 0.382 * sin(0 - 3*0.172 + /4)   =   -0.28335  m . (c)   wavelength = 2 / k = 2 / 3   = 0.6667 m .        frequency = / 2 = 14 / 2  =   7.00Hz . (d) max mag of trans speed = A = 0.382 * 14 =    16.8 m/s

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