Question

A sinusoidal sound wave moves through a medium and is described by the displacement wave function

s(x,t) = (2.00µm)cos[(15.7 rad m )x − (858 rad s )t].

a) Find the amplitude of this wave.

b) Find the wavelength of this wave.

c) Find the speed of this wave.

d) Determine the instantaneous displacement from equilibrium of the elements of the medium at the position x = 0.0500 m and t = 3.00 ms.

e) Determine the maximum speed of the element’s oscillatory motion.

Answer 1

sound wave displacement wave function,

s(x,t)=(2um)cos[(15.7)x-(858)t]

general form of displacement wave function is

s(x,t)=A*cos(k*x-w*t)

by comparing above two equation,

a)

amplitude A=2um =2*10^-6 m

b)

wave length, lambda=2pi/K

=2pi/(15.7)

=0.4 m

c)

wave speed v=w/k

v=858/(15.7)

v=54.65 m/sec

D)

s(x,t)=(2um)cos[(15.7)x-(858)t]

at x=0.05m , t=3*10^-3 sec

s(x,t)=(2*10^-6)cos((15.7)*0.05-(858)*3*10^-3)

displacement,

s=1.99*10^-6 m

or

s=2*10^-6 m

s=2um

E)

maximum speed of the element is,

v=A*w

v=2*10^-6*(858)

v=1716*10^-6 m/sec

v=1.72*10^-3 m/sec