Transcript Doppler Effect - 首頁 - 廖寶珊紀念書院 Liu Po

Doppler
Effect
Liu Po Shan Memorial College
Chan Yick Nam
Warm-up Activity
 Watch
the movie . . .
 What is Doppler Effect ?
Summary .. 1
The Doppler effect is . . .
the apparent change in the frequency
of a wave motion
when there is relative motion
between the source and the observer.
Moving Source
 Watch
the Flash Animation . . .
 What is the effect when the source is
moving ?
Moving Source

2
1
vS
Stationary Source
Moving Source
Follow-up Activity
 Watch
the movie again . . .
 Explain why the pitch of the whistle
changes as the car passes the observer ?
Explanation to movie
Stationary Source

c=f
c
=
f
Stationary Source
Moving Source - Change in 
2
c - vS
1 =
f
1
vS
Moving Source
c + vS
2 =
f
Source Moving Toward Observer
1
vS
O1
c - vS
1 =
f
c
f1 =
1
c
f
f1 =
c - vS
The wavelength becomes SMALLER
The observed frequency becomes HIGHER
Source Moving Away From Observer
2
O2
v
vS
c + vS
2 =
f
c
f2 =
2
c
f
f2 =
c + vS
The wavelength becomes LARGER
The observed frequency becomes LOWER
Moving Source


Watch the JAVA animation . . .
What is the change in wavelength
when the speed of the moving source
changes ?
Summary ... 2A


The wavelength changes when the
source moves.
The wave speed is independent of
the speed of source.
Apparent Frequency –
Moving Source
Watch the FLASH animation . . .
 Notice the different frequency
observed by stationary observers.

Change in Observed Frequency
c
f
f1 =
c - vS
c
f - f
f = f1 - f =
c - vS
vS
f
f =
c - vS
vS
f
If vs << v then
=
c
f
S
O1
Summary ... 2B


The apparent frequency observed by the
observer changes.
For the source moving TOWARD the
observer,
•
•

The wavelength reduces.
The apparent frequency increases.
For the source moving AWAY the observer,
•
•
The wavelength increases.
The apparent frequency decreases.
Moving Observer
Watch the Flash Animation . . .
How does the frequency of the wave
observed change when the observer is
moving ?
Apparent Frequency
– Moving Observer
Compared with the stationary observer:
– Observer moving toward the source encounter
more waves in each second. So the observer
observes higher frequency. Apparent
frequency increases.
– Similarly, observer moving away from the
source encounter less waves in each second.
Therefore the apparent frequency decreases.
Apparent Frequency (moving Observer)
– Relative Velocity
For moving observer,
the apparent frequency results from the
change in relative velocity of the sound to
the observer.
the wavelength does not change with the
motion of the observer.
Moving Observers
c + vo
f1 =
f
c
O2
O1
vo
S
Stationary
Source
vo
c - vo
f
f2 =
c
Change in Observed Frequency
c + vo f
f1 =
c
c + vO
f - f
f = f1 - f =
c
vo f
f =
c
vo
f
=
c
f
O
Summary ... 3



The apparent change in frequency f is
known as the Doppler Shift.
The Doppler shift increases as the relative
velocity between the source and the
observer increases.
The Doppler effect applies to all forms of
waves.
Moving Observer and
Moving Source
• Moving Source
 change in   f
• Moving Observer
 change in relative velocity  f
• Moving Source and Observer
 change in  and relative velocity  f
Equations –
Moving Source and Observer
vs
S
vo
vo
vs
S
O
 c  vo 
 f
f '  
 c  vs 
 c  vo 
 f
f '  
 c  vs 
vs
S
vo
vs
O
 c  vo 
 f
f '  
 c  vs 
O
vo
S
O
 c  vo 
 f
f '  
 c  vs 
Combining the Equation
Mathematically,
c  vo
f ' (
)f
c  vs
The observed frequency of wave is increased when
the source and observer are approaching each other
and is decreased when they are receding from each
other.
ONE Equation for ALL cases
One Equation
 c  vo 
 f
f '  
 c  vs 
Method to Assign Sign
Step 1:
Assign the direction from source to observer be positive
Step 2:
If the velocities are in the positive direction,
vo and vs are set to be positive.
If the velocities are in the negative direction
vo and vs are set to be negative.
Step 3:
Put the values of vo and vs with sign into the above equation