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Friday #3
Wave Propagation
Wave propagation on ropes and strings depends on the two ingredients of inertia and
linear restoring force.
For a rope or string we define its inertia in terms of how much
mass there is for a given length.
We will use the symbol
W
for this, and it is measured in
units of kilograms per meter.
The restoring force depends on the tension force – how
tightly it is strung.
For tension force we will use the symbol
F
and it is measured in
Newtons=
2
/sec
Kg m
⋅
.
The wave speed is given by:
F
v
W
=
The ratio of
F/W
has the units of
2
2
()
sec
sec
Kg m m
m
Kg
⋅
⋅
=
so its squareroot has the units of
speed.
There is a close similarity between this formula and the formula for the speed of sound in
air.
The linear restoring force is provided by the air pressure and the inertia is provided
by the mass density of the air.
The in the ratio, the number density of atoms cancels out
so that the main dependence is on the absolute air temperature
T
and the average mass per
atom
M
.
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This note was uploaded on 03/30/2008 for the course 029 044 taught by Professor Skiff during the Spring '08 term at University of Iowa.
 Spring '08
 SKIFF

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