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Doppler Effect
Introduction
 As
shown in the diagram to the left, the observed frequency is different from the
source frequency if the source is moving compared to the observer.
The observer hears at higher frequency if the source is
moving toward the observer. As shown in the diagram to the left, there are
more waves hitting in the same time period.
The observer hears a lower frequency if the source is moving
away from the observer. There are fewer waves hitting in the same time
period.
 When
the source moves closer to the observer, the second wave is not created until
the source is closer to the observer. The wavelength of sound getting to
the observer is decreased by the distance traveled between when the first wave
and second wave are created.
A similar process occurs if the source is stationary and the
observer is moving.
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f' = frequency of observer
f = frequency of source
v = velocity of sound in air
vo = velocity of observer
vs = velocity of source |
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The upper signs apply if the source and
observer are moving toward each other.
The lower signs apply if the source and observer are moving away
from each other. |
Table of Contents
Problems
| 1. |
In on of the original Doppler
experiments, one tuba was played on a moving platform car at a frequency
of 75.0 Hz, and a second identical tuba played the same tone while at
rest in the railway station. What beat frequency was heard as the
train approached the station at a speed of 10.0 m/s? The temperature
is 20.oC.
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| 2. |
Two train whistles at 277 Hz
each are blown. One train is at rest and the second is moving away
at 40.0 km/h from the observer at rest. What beat frequency with the
observer hear? The temperature is 20.oC.
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| 3. |
A horn is blown at 350. Hz on a
train moving North at 65 km/h. (a) What frequency is heard in a car
moving North at 95 km/h? (b) What frequency is heard if
the car is moving South at 95 km/h? The temperature is 20.oC.
The car is North of the train at the start.
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| 4. |
A bat at rest emits ultrasound
waves at 50.0 kHz and receives them in return from an object moving away
radially at 25.0 m/s. What is the received sound frequency?
The temperature is 20.oC. |
Table of Contents
Answers
| 1. |
In on of the original Doppler
experiments, one tuba was played on a moving platform car at a frequency
of 75.0 Hz, and a second identical tuba played the same tone while at
rest in the railway station. What beat frequency was heard as the
train approached the station at a speed of 10.0 m/s? The temperature
is 20.oC.
|
|
f = 75 Hz
v = 343 m/s
vo = 0 m/s Observer
is Stationary
vs = 10.0 m/s
343 m/s + 0 m/s
f ' = 75.0 Hz ( --------------------------
) = 77.3 Hz
343 m/s - 10.0 m/s
Beat frequency = f '
- f = 77.3 Hz - 75.0 Hz = 2.3 Hz
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f ' is frequency heard by observer
on the platform
f is the frequency of the source
Since they are moving toward each other,
we will use the top set of signs. |
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| 2. |
Two train whistles at 277 Hz
each are blown. One train is at rest and the second is moving away
at 40.0 km/h from the observer at rest. What beat frequency with the
observer hear? The temperature is 20.oC.
|
|
40.0
km 1000
m 1 h
----------- x ----------- x ----------- =
11.1 m/s
1
h
1 km 3600 s
f = 277 Hz
v = 343 m/s
vo = 0 m/s Observer
is Stationary
vs = 10.0 m/s
343 m/s - 0 m/s
f ' = 277 Hz ( ---------------------------
) = 268 Hz
343 m/s + 11.1 m/s
Beat frequency = f '
- f = 277 Hz - 268 Hz = 9 Hz
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f ' is frequency heard by observer on the platform
f is the frequency of the source
Since they are moving away from each
other, we will use the bottom set of signs.
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| 3. |
A horn is blown at 350. Hz on a
train moving North at 65 km/h. (a) What frequency is heard in a car
moving North at 95 km/h? (b) What frequency is heard if
the car is moving South at 95 km/h? The temperature is 20.oC.
The car is North of the train at the start.
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343
m 1
km 3600
s
--------- x ----------- x ----------- =
1230 km/h
1
s 1000
m 1 h
f = 350 Hz
v = 1230 km/h
vo = 95 km/h
vs = 65 km/h
1230 km/h
- 95 m/s
f ' = 350 Hz (
-------------------------------- ) = 341 Hz
1230 km/h
- 65 m/s
1230 km/h
+ 95 m/s
f ' = 350 Hz (
-------------------------------- ) = 398 Hz
1230 km/h
- 65 m/s
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f ' is frequency heard by
observer on the platform
f is the frequency of the source
(a) Since the car is moving away
from the train, we will use the bottom sign for the velocity of the
observer.
Since the train is moving away from the
car, we will use the top sign for the source.
(b) Since both the train and the car are
moving toward each other, we will use the top sign for both. |
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| 4. |
A bat at rest emits ultrasound
waves at 50.0 kHz and receives them in return from an object moving away
radially at 25.0 m/s. What is the received sound frequency?
The temperature is 20.oC.
|
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f = 50.0 kHz
v = 343 m/s
vo = 25.0 m/s
vs = 0 m/s
343 m/s
- 25.0 m/s
f ' = 50.0
kHz(
----------------------------- ) = 46.4 Hz
343 m/s
+ 0 m/s
f = 46.4 kHz
v = 343 m/s
vo = 0 m/s
vs = 25.0 m/s
343 m/sh
- 0 m/s
f ' = 46.4 Hz (
-------------------------------- ) = 43.2 Hz
343 m/s
+ 25.0 m/s
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First calculate the frequency received by the
object moving away from the bat.
We use the bottom signs since they are
moving away.
This is the frequency that is reflected
back to the bat.
Now calculate the frequency received by
the bat.
They are moving away from each other and
we use the bottom signs.
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Table of Contents
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