Transcript DOPPLER EFFECT

Harmonics
Strings as Harmonic Oscillators
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Its mass gives it inertia
Its tension and curvature give it a
restoring force
It has a stable equilibrium
Its restoring force is proportional to
displacement
Modes of Oscillation
Fundamental Vibration (First Harmonic)
 String simply vibrates up and down
 Frequency of vibration ( pitch) is
 proportional to tension
 inversely proportional to length
 inversely proportional to density
Harmonic Series
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A series of
frequencies that
includes the
fundamental
frequency and
integral
multiples of the
fundamental
frequency.
λ = 2L , f 1
λ2 = L , f
2
=2
λ3 = 2/3 L , f
3
f1
=3f
1
To Calculate the harmonic series of
standing waves on a vibrating string
harmonic number
fn = n (ν/2L)
frequency
Air Column as Resonant System
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A column of air is a
harmonic oscillator
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Its mass gives it inertia
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Pressure gives it a
restoring force
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It has a stable
equilibrium
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Restoring forces are
proportional to
displacement
f0
2f0
3f0
Air Column Properties
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An air column vibrates as a single object
 Pressure node occurs at center of open
column
 Velocity antinode occurs at ends of open
column
Pitch (frequency of vibration)
 inversely proportional to column length
 inversely proportional to air density
Length
Length
Air Column Properties
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Just like a string,
an open air
column can
vibrate at many
different
frequencies
(harmonics).
fn = n (ν/2L)
Air Column Properties
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A pipe with 1
closed end
only generates
odd
numbered
harmonics
pressure
nodes
occurs at
sealed end
λ = 4L
λ 3 = 4/3 L
λ 5 = 4/5 L
Calculating the harmonic series of
standing waves on a closed pipe
harmonic number
fn = n (ν/4L)
frequency