The Wave part of Phys 103

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The Wave part of Phys 103
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Wave Propagation
A wave is a disturbance in an elastic medium
which travels, or propagates through the medium.
The wave is intangible. The medium itself does
not travel, but only oscillates back and forth.
So there is not a net transport of matter from
place to place. However, a wave transports energy
from place to place, through the medium. Waves
come in many forms, all with certain common
properties. There are waves in a plucked string,
seismic waves, sound waves, electromagnetic
waves. These are different sorts of disturbances
propagating in different sorts of media. In this
course, we will consider the common properties.
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Wave Motion
y is the displacement from equilibrium at
position x and at time t. f is an unspecified
function.
i) wave speed is a property of the medium. ii)
shape of the wave pulse is unchanged as it
travels iii) two or more wave pulses that exist
at the same place time in a medium
addsuperimpose.
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Harmonic wave a wave of a particular shape that
repeats itself. Its periodic.
Each point in the medium (x) is displaced from
equilibrium (y). As time passes, the pattern is
shifted by a phase factor the wave
pattern moves through the medium.
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superposition
reflection
Standing waves
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Stretched string
Only vibrations that fit in the length of the
string will persist. This is an example of
resonance. Every physical system has natural
modes at which it will vibrate. The natural
modes depend on the physical properties of the
system mass, elasticity, size. We saw this same
phenomenon with the spring and the pendulum.
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Beats
In this case, two waves are traveling in the same
direction, but with slightly different
frequencies.
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Spectrum
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Energy
.
While the medium in which the wave propagates
does not flow from one place to another, the wave
disturbance nonetheless carries energy from one
place to another. Each mass element, dm, of the
medium executes simple harmonic motion. K is the
restoring force constant. Its related to the
frequency by
Over one cycle, the cosine-squared and
sine-squared average to
. The total mass of the medium spanning one cycle
(or one wavelength) is
, where
is the mass per unit length of the medium.
In terms of the wave speed, c,
.The energy flux is the power transported through
the medium by the wave
The intensity is the power pr unit area through
which the power is transported
, were
is the mass per unit volume.
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Pressure waves--Sound
Compression, or longitudinal waves. Medium
oscillates parallel to direction of
propagation. Pressure amplitude, yp. Speed of
sound waves depends on density, pressure,
temperature elasticity of the medium. Doppler
effect. . . . deciBels. . .
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