LO 1 Sound Wave: Calculate speed of sound in a material based on bulk modulus and density

1. Sound Waves: Calculate speed of sound in a material based on bulk modulus and
desnity.
Question:
a) What is the speed of a sound wave in liquid mercury (Bulk modulus (B):
2.85x10^10 Pa. Density: 13 534kg/m^3) with a frequency of 1012Hz?
b) What would be the amplitude of pressure variation (delta p_m) given that the
sound wave has a displacement amplitude (s_m) of 1.1x10^-11m.
c) Compare the equations of displacement and pressure variations; they are
___________ by ______ rad.
Solution:
a) Velocity = sqrt(bulk modulus/density of medium)=sqrt(2.85x10^10Pa/13
534kg/m^3)~ 1450m/s
b) Delta p_m= Bks_m. B and s_m are given. To plug in the value of k
(k=2pi/wavelength), first determine the wavelength using the equation;
wavelength= velocity (from part a)/frequency. Wavelength~1.433 m
therefore k~4.385. Solving for delta s_m you get approximately 1.375m.
c) s(x,t)=s_m*cos(kx-omega*t+phi)
deltap=Bks_m*sin(kx-omega*t+phi)
Plugging in all the given and calculated terms, one can observe that these
equations are different in the sense that displacement is a cosine function
and pressure is a sine function but their arguments are the same. There for
the are out of phase by pi/2 rads.