please solve part b c and d A sinusoidal sound wave moves through a medium and i

Question

please solve part b c and d

A sinusoidal sound wave moves through a medium and is described by the displacement wave function s(x, t) = 2.18 cos(15.0x-862) where s is in micrometers, x is in meters, and t is in seconds. (a) Find the amplitude of this wave. 2.18 (b) Find the wavelength of this wave. X cm (c) Find the speed of this wave. X m/s (d) Determine the instantaneous displacement from equilibrium of the elements of the medium at the position x0.049 9 m at t= 2.93 ms. the maximum speed of a element's oscillatory motion. 1.87916 mm/s

Explanation / Answer

a) amplitude A = 2.18 micro m

b) here wave number k = 2pi/lambda = 15

lambda = 2*3.14/15 = 0.419 m = 41.9 cm

c) v = w/k = 862/15 = 57.5 m/s

d) s = 2.18cos(15*0.0499-862*2.93*10^-3) = 0.46*10^-6 m

e) v max = Aw = 2.18*10^-6*862 = 1.879 mm/s

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