To practice problem solving with mechanical waves. Based on Young/Freedman Probl

Question

To practice problem solving with mechanical waves. Based on Young/Freedman Problem-Solving Strategy 15.1 Waves on a string are described by the following general equation y(x, t) - A sin (kx - omega t) A transverse wave on a string is traveling in the +x direction with a wave speed of 9.00 m/s, an amplitude of 7.50 times 10^-2 m, and a wavelength of 0 470 m. At time t = 0, the x = 0 end of the string has zero displacement. Find the transverse displacement y of a particle at x = 1 30 m and t = 0.150 s Find the transverse displacement y of a particle at x = 1.30 m at time t = 0, 150 s, Express your answer in meters. y =

Explanation / Answer

given

A= 7.50 * 10^-2 m

v = 9.0 m/s

lamda = 0.470 m

k = 2pi/ lamda = 2pi/0.470 m = 13.36

v= w/k

w= vk = 9.0 (13.36) = 120.25 rad/s

y = A sin ( kx- wt)

= 7.5 * 10^-2 * sin ( 13.36 ( 1.3) - ( 120.25(0.150))

=-4.65 * 10^-2 m

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