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Unformatted text preview: embrane
at x = 0.) The fluids have bulk moduli and densities B1, ρ1 for x < 0 and B2, ρ2 for x > 0.
The characteristic impedance of either fluid is Z = ρv = (Bρ)1/2, where the wave speed
in the fluid is v =
x<0 x>0 A sound wave of the form s(x,t) = f(x-v1t) (for x ≤ 0) is incident on the interface between
the fluids from the left. Based on what we found for the change in medium with
transverse waves on strings, we expect that
for x ≤ 0:
for x ≥ 0:
where R and T are the reflection and transmission coefficients. (Note that R<0 in this
case means the displacements in the reflected wave are opposite in direction to those in
the incident wave.)
(a) To solve for R and T we need two boundary conditions. The first is that at x=0, the total
displacements on either side of the membrane must be the same (why?). Use this fact to
show that 1 + R = T.
(b) The other boundary condition comes from Newton's 3rd law: the force exerted by fluid 1
on fluid 2 must be equal an...
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This note was uploaded on 02/27/2013 for the course PHY 2214 taught by Professor Davis during the Spring '12 term at Cornell University (Engineering School).
- Spring '12