bulk modulus

In a longitudinal wave the constituents of the
medium oscillate forward and backward in the
direction of propagation of the wave. We have
already seen that the sound waves travel in the
form of compressions and rarefactions of small
volume elements of air. The elastic property that
determines the stress under compressional
strain is the bulk modulus of the medium defined
by (s'


ee chapter 9)P
B
V/V
(15.16)
Here the change in pressure ΔP produces a
volumetric strain
V
V
. B has the same dimension
as pressure and given in SI units in terms of
pascal (Pa). The inertial property relevant for the
propagation of wave in the mass density ρ, with
dimensions [ML–3]. Simple inspection reveals
that quantity B/ρ has the relevant dimension:
–1 –2
2 –2
–3
M L T
L T
M L
(15.17)
Thus if B and ρ are considered to be the only
relevant physical quantities,
v = C B
(15.18)
where, as before, C is the undetermined constant
from dimensional analysis. The exact derivation
shows that C=1. Thus the general formula for
longitudinal waves in a medium is:
v = B
ρ