LECTURE 7
DOPPLER EFFECT, SUPERPOSITION AND
INTERFERENCE OF WAVES
Instructor: Kazumi Tolich
Lecture 7
2
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Reading chapter 14.6 to 14.7
¤ Doppler
effect
¤ Superposition
¤ Interference
Quiz: 1
3
¨
Observers A, B, and C listen to a sound form a moving source. The
locations of the sound wave crests at a given moment are shown in the
figure. Rank the observer according to the frequency of the sound,
smallest first.
Quiz: 7-1 answer
4
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¨
¨
¨
¨
A<B<C
The wavelength of the sound wave is indicated by the distance
between two neighboring crests.
At C, the crests are closer together, indicating the smaller
wavelength.
'
Thus the observed frequency is highest at C since 𝑓 = , where
(
𝑣 is the speed of the sound which is common for all observers.
This shift in frequency (or wavelength) due to the motion of the
wave source and/or observer is called the Doppler effect.
The Doppler effect/Demo: 1
5
¨
Shifted frequency, 𝑓 * , in sound
can be observed when the source
is moving, the observer is moving,
or both are moving with respect to
the medium.
𝑓*
¨
𝑢.
1 ± 𝑢. ⁄𝑣
=
𝑓
1 ∓ 𝑢1 ⁄𝑣
𝜆*
Demo: siren on a string
𝑢1
Sonic boom
6
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¨
The Doppler shifts for a moving source and a
moving observer cases are similar for low speeds
but then diverge.
If the source moves faster then the speed of
sound, a sonic boom is created.
Applications of the Doppler effect
7
¨
¨
The Doppler shift is observed in electromagnetic waves as well.
The Doppler effect has many practical applications: weather radar, speed
radar, medical diagnostics, astronomical measurements.
Quiz: 2
¨
Amy and Zack are both listening to a sound wave from a
source that is moving to the right. Rank the frequencies that they
hear and the source frequency, smallest first.
Quiz: 7-2 answer
¨
𝑓345 = 𝑓6 < 𝑓789:
¨
𝑓* =
¨
Since the source is moving toward receiver Zack, and Zack (receiver) is moving
;±<= ⁄'
;∓<> ⁄'
𝑓
toward the source, he hears 𝑓789: =
¨
;? ;6 4⁄1 ⁄'
;A ;6 4⁄1 ⁄'
𝑓6 > 𝑓6
Since the source is moving away from the receiver Amy, and Amy (receiver) is
moving toward the source, she hears 𝑓345 =
;? ;6 4⁄1 ⁄'
;? ;6 4⁄1 ⁄'
𝑓6 = 𝑓6
Example 1
10
¨
You are standing by a road, and a
police car passes by. The
frequency of a police siren is
550 Hz as the police car
approaches you, and 450 Hz
after it passes you and is receding.
If the speed of sound is 343 m/s,
how fast is the police car
traveling?
Principle of Superposition
11
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¨
Waves of small amplitude traveling through the same medium combine, or
superpose, by simple addition.
If two pulses combine to give a larger pulse, this is constructive interference (a). If
they combine to give a smaller pulse, this is destructive interference (b).
Quiz: 3
¨
Two identical waves with the same phase are added. Which of the following
statements is/are correct about the resultant wave? Choose all that apply.
A.
B.
C.
D.
E.
F.
G.
Its frequency is the same as that of the original waves.
Its frequency is doubled.
Its frequency is zero.
Its amplitude is the same as that of the original waves.
Its amplitude is doubled.
Its amplitude is zero.
This problem cannot be solved without knowing the wavelengths of the two waves.
Quiz: 7-3 answer
¨
¨
Its frequency is the same as the added waves.
Its amplitude is doubled.
Constructive
Destructive
Interference patterns
14
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Two-dimensional waves exhibit interference pattern.
If the sources are in phase, constructive interference
occurs if the path length difference, ∆𝑟, is 0, 𝜆, 2𝜆, 3𝜆, ⋯,
and destructive interference occurs if ∆𝑟 is JK𝜆, LK𝜆, MK𝜆 , ⋯
4λ
5λ
4λ
4.5λ
Quiz: 4
15
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Speakers A and B are right next to each other and emit sound waves
with a wavelength of 𝜆 = 1 m, which interfere constructively at a
donkey located far away (say, 200 m). What happens to the sound
intensity if speaker A steps back 2.5 m?
A.
B.
C.
D.
Intensity increases
Intensity stays the same
Intensity goes to zero
Impossible to tell
A
B
𝐿
Quiz: 7-4 answer/Demo: 2
16
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¨
¨
¨
¨
Intensity goes to zero
If 𝜆 = 1 m, then a shift of 2.5 m corresponds to 2.5𝜆,
which puts the two waves out of phase, leading to
destructive interference.
The sound intensity will therefore go to zero.
Follow-up: What if you move back by 4 m?
Two Speaker Interference
¤
Demonstration of constructive and destructive interference
due to path length differences.
eir amplitudes sum.
nterval of 0.10 s. Draw the pulses at the indicated later times and add
ment of point P at those times.
l to
Example: 2 (Walker Ch. 14-57)
17
A pair of in-phase stereo speakers is
placed side by side, separated by a
distance of 𝐿 = 0.914 m. You stand
directly in front of one of the speakers,
𝑑; = 2.44 m from the speaker. What is the
lowest frequency that will produce
When wave pulses collide, they pass right through each
constructive interference at your location?
¨
o
ach other.
ers are 0.914 m
e of the speakers.
not drawn to scale.
0.914 m
13. Use the
from the second
stance d1 to the
ath length for the
o one wavelength
y.
2
d
2.44 m
d2
d1 = 2.44 m
2
0.914 m
2
2.606 m