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The wave function for a traveling wave on a taut string is (inSI units) the foll

ID: 1745656 • Letter: T

Question

The wave function for a traveling wave on a taut string is (inSI units) the following equation. y(x, t) = (0.368 m)sin(8t - 1x +/4) (a) What are the speed and direction oftravel of the wave?
m/s Directionpositive x-directionpositive y-directionpositive z-directionnegative x-directionnegative y-directionnegative z-direction
(b) What is the vertical position of an element of the string att = 0, x = 0.120m?
m

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

(d) What is the maximum magnitude of the transverse speed of thestring?
m/s y(x, t) = (0.368 m)sin(8t - 1x +/4) (a) What are the speed and direction oftravel of the wave?
m/s Directionpositive x-directionpositive y-directionpositive z-directionnegative x-directionnegative y-directionnegative z-direction
(b) What is the vertical position of an element of the string att = 0, x = 0.120m?
m

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

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

Explanation / Answer

Given y(x, t) = (0.368 m)sin(8t - 1x +/4) compare this with y = A sin ( t - k x + ) we get propagation constant k = angular frequency = 8 amplitude A = 0.368 m (a). speed v = / k                     = 8 m / s (b). the vertical position of an element of the string att = 0, x = 0.120 mis   y = 0.368 m sin [ 8* 0 - *0.12 +/ 4]                                                                                                                     = -0.09524 m (c). wavelength = 2 / k                           = 2 m (d). frequency f = / 2                         = 4 Hz (d). maximum magnitude of the transverse speed of the string =A                                                                                             =9.248 m / s