Question

A sinusoidal sound wave is described by the displacement s(x, t) = (1.82 µm) cos[(15.0 m-1)x - (878 s-1)t]

(b) Determine the instantaneous displacement of the molecules at the position x = 0.0503 m at t = 3.03 ms. (answer in µm)
(c) Determine the maximum speed of a molecule's oscillatory motion. (answer in mm/s)

Answer 1

given that

s(x, t) = (1.82 µm) cos[(15.0 m-1)x - (878 s-1)t]

at x = 0.0503 m

and t = 3.03 ms

then s(x,t) = (1.82um)*cos((15*0.0503)-(878*3.03)) = -0.41 um

b) v_max = A*w = 1.82*10^-6*878 = 1.59796*10^-3 m/sec = 1.59796 mm/sec