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Unformatted text preview: Dispersion rel’n function depends on the wave type
and medium.
E.g. deep water waves: ωdeep water
vphase ω
≡
k vgroup
≈ gk dω
≡
dk We’ll discuss the physical distinction between them
later.
Wednesday, October 9, 2013 D.A. quiz question
MASS, LENGTH, TIME
Want to make a velocity, using only g, lambda
and maybe the density rho. Velocity has units
of length over time. Lambda has units of length
g has units of length over timesquared. rho has
units of mass over lengthcubed. The units do
not allow rho to enter, since no way to cancel
its mass. Velocity units can be obtained only as
v∼
Wednesday, October 9, 2013 gλ ∼ g
k (v2 /v1 ) = g2 λ2 /g1 λ1 Standing waves
=Superposition of left + right moving wave
Here, person makes right
moving wave, and the B.C.
at the other end reﬂects it
back, total is standing wave
A cos(kx − ω t) + A cos(kx + ω t) = 2A cos(kx) cos(ω t) To the right + To the left = “Standing”
cos(a ± b) = cos a cos b ∓ sin a sin b
useful trig.
sin(a ± b) = sin a cos b ± cos a sin...
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This note was uploaded on 02/11/2014 for the course PHYSICS 2C taught by Professor Hicks during the Fall '09 term at UCSD.
 Fall '09
 Hicks
 Energy

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