A sinusoidal sound wave moves through a medium and is described by the displacem
ID: 1576908 • Letter: A
Question
A sinusoidal sound wave moves through a medium and is described by the displacement wave function
s(x, t) = 2.20 cos(15.6x 888t) where s is in micrometers, x is in meters, and t is in seconds.
(a) Find the amplitude of this wave. _____ µm
(b) Find the wavelength of this wave. ______ cm
(c) Find the speed of this wave. ______ m/s
(d) Determine the instantaneous displacement from equilibrium of the elements of the medium at the position x = 0.049 7 m at t = 2.99 ms. _____ µm
(e) Determine the maximum speed of a element's oscillatory motion. _____ mm/s
Explanation / Answer
give wave equation s(x , t) = 2.2cos(15.6x - 888t)
standard wave equation s(x , t) = Acos(kx - wt)
(a)
amplitude A = 2.2 um
(b)
wavelength lambda = 2pi/k = 2pi/15.6 = 0.403 m = 40.3 cm
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(c)
speed v = w/k = 888/15.6 = 57 m/s
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(d)
s(x , t) = 2.2cos(15.6*0.0497 - 888*2.99*10^-3) = -0.669 um
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(e)
maximum speed v = w*A = 888*2.2*10^-6 = 1.95 mm/s