Understanding Interference and Beats in Waves

 
Interference and beats
Interference and beats
 
1
 
Two overlapping waves
interfere with each other
 
2
 
11-11 Interference; Principle of Superposition
 
Constructive
interference
 
3
 
11-11 Interference; Principle of Superposition
 
Destructive
interference
 
Constructive
interference
 
4
 
11-11 Interference; Principle of Superposition
 
Destructive
interference
 
Constructive
interference
 
Somewhere
in between
 
5
Two overlapping waves
interfere with each other
 
Constructive interference at C
6
Two overlapping waves
interfere with each other
 
Destructive interference at D
7
 
Interference of Sound Waves: Beats
 
Waves can also interfere in time, causing a phenomenon called beats. Beats are
the slow 
envelope
 around two waves that are relatively close in frequency.
 
8
 
Beat frequency = difference in frequency of the two waves
Waves can also interfere in time, causing a phenomenon called beats. Beats are
the slow 
envelope
 around two waves that are relatively close in frequency.
Interference of Sound Waves: Beats
9
 
https://youtu.be/IQ1q8XvOW6g
 
https://youtu.be/TrpQX5uKxQY
 
Interference of sound waves: Beats
 
10
 
Beat frequency = difference in frequency of the two waves
 
Waves can also interfere in time, causing a phenomenon called beats. Beats are
the slow 
envelope
 around two waves that are relatively close in frequency.
 
Interference of Sound Waves: Beats
 
11
12-52
: Two piano strings are supposed to be vibrating at 220Hz , but a piano tuner hears
three beats every 3.5s when they are played together. If one is known to be vibrating
at 220Hz , what must be the frequency of the other? Is there only one answer?
 
The other string must vibrate at
 
The beat frequency is
 
or
12
 
The Doppler effect
The Doppler effect
 
13
 
A stationary observer hears a firetruck’s siren change in pitch as it drives by
The Doppler effect occurs when a source of sound
moves with respect to an observer
14
 
They detect the same frequency
Firetruck at rest
Observer at rest
Observer at rest
15
They detect the same frequency
 
Detects a lower frequency
and longer wavelength
 
Detects a higher frequency
and shorter wavelength
Firetruck at rest
Firetruck moving
Observer at rest
Observer at rest
16
The same thing happens if the truck is at rest and the observers move
 
This person encounters more
wavefronts per second when moving
towards the truck than when standing still
 
Therefore measures a higher frequency
 
This person encounters fewer
wavefronts per second when moving
away from the truck than when standing still
 
Therefore measures a lower frequency
Firetruck at rest
17
The Doppler effect
 
The frequencies are related as follows
 
The upper signs apply if the source and observer move CLOSER TOGETHER
The lower signs apply if the source and observer MOVE APART
 
…and the sound
source and/or the
observer moves, and:
 
Suppose:
 
is the speed of
sound
18
 
iClicker Question
 
19
 
Two people are moving closer together. Each will
hear the other’s voice
A
 
with a lower pitch
B
 
with a higher pitch
C
 
the same as when they were motionless
D
 
in a higher amplitude
E
 
in a lower amplitude
Example 12-15
: The siren of a police car at rest emits at a predominant
frequency of 1600 Hz. What frequency will you hear if you are at rest
and the police car moves at 25 m/s (a) towards you, and (b) away from you?
 
(a) You and the police car are moving closer together: Use the upper signs
20
Example 12-15
: The siren of a police car at rest emits at a predominant
frequency of 1600 Hz. What frequency will you hear if you are at rest
and the police car moves at 25 m/s (a) towards you, and (b) away from you?
(b) You and the police car are moving apart: Use the lower signs
21
Example 12-15
: The siren of a police car at rest emits at a predominant
frequency of 1600 Hz. What frequency will you hear if you are at rest
and the police car moves at 25 m/s (a) towards you, and (b) away from you?
 
So, as the car approaches and moves past you, you hear the siren drop in pitch.
 
Specifically, it goes from                   to
22
12.57: A bat at rest sends out ultrasonic sound waves at 46.5kHz and receives them
returned from an object moving directly away from it at 31.5m/s .
What is the received sound frequency?
 
The upper signs apply if the source and observer move CLOSER TOGETHER
The lower signs apply if the source and observer MOVE APART
 
Assume the bat is at rest.
 
Bat
 
Object
 
The frequency received by the object is
23
12.57: A bat at rest sends out ultrasonic sound waves at 46.5kHz and receives them
returned from an object moving directly away from it at 31.5m/s .
What is the received sound frequency?
 
Next, the sound bounces off the moving object and returns to the bat.
 
So now we have a moving source and a stationary observer
24
12.57: A bat at rest sends out ultrasonic sound waves at 46.5kHz and receives them
returned from an object moving directly away from it at 31.5m/s .
What is the received sound frequency?
The upper signs apply if the source and observer move CLOSER TOGETHER
The lower signs apply if the source and observer MOVE APART
 
Assume the bat is at rest.
 
Bat
 
Object
 
The frequency received by the bat is
25
 
So, the bat gets information about the object (e.g., an insect):
 
How far away it is (time for the signal to return)
 
Which way it is going and how fast (Doppler shift)
 
26
 
Measuring sound reflections is the basis of sonar (“
s
ound 
na
vigation
r
anging”)
 
Locate things underwater
Geology
 
The method is also used in medical applications in combination
 
with the Doppler effect
 
The emitted and received signal can be mixed and the resulting beats
can be measured
 
Example: Monitoring the location, movements, and heartbeat of a fetus
27
 
Where does the Doppler formula come from?
Where does the Doppler formula come from?
 
28
Source
Wavefronts
 
The time between emissions is
 
Recall
 
and therefore
The Doppler effect
29
 
Source
 
The Doppler effect
 
Now suppose that the source moves
toward the right with speed
 
30
Source
The Doppler effect
Now suppose that the source moves
toward the right with speed
 
This shortens the distance between the
emitted wavefronts, so that
 
Recall that:
 
In time T, it moves a distance
31
Source
The Doppler effect
 
This is the wavelength that would be
measured by a stationary observer
 
Observer
 
The observer would perceive
a frequency given by
32
Source
The Doppler effect
Observer
This is valid when the source
moves 
TOWARDS
 the observer:
 
Notice:
33
Source
The Doppler effect
Observer
If the source moves 
AWAY
 from
 the observer, the same argument
goes through but with a sign change
(go back and check!!):
 
Notice:
34
Source
The Doppler effect
Observer
We can combine these results:
 
Source moves 
toward
 observer: upper sign
Source moves 
away from
 observer: lower sign
35
The Doppler effect
What if the source is stationary, but the observer moves?
 
Source
 
Observer
 
Here, the observer moves towards
the source.
From the observer’s perspective,
the sound waves move at speed
 
Thus the observer detects a frequency
36
 
The Doppler effect
 
What if the source is stationary, but the observer moves?
 
Source
 
Observer
 
Here, the observer moves 
TOWARDS
the source.
 
37
 
The Doppler effect
 
What if the source is stationary, but the observer moves?
 
Source
 
Observer
 
Here, the observer moves 
AWAY
from the source.
 
38
 
The Doppler effect
 
All these results can be combined into this equation:
 
The upper signs apply if the source and observer move CLOSER TOGETHER
 
The lower signs apply if the source and observer MOVE APART
 
39
 
THE END of Chapter 12
 
40
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Explore the fascinating phenomena of interference and beats in waves, where overlapping waves interact to create patterns of constructive and destructive interference. Witness how sound waves can also produce beats when interfering in time, resulting in a slow envelope effect. Delve into the principles of superposition and discover the concept of beat frequency as the difference in frequency between two interfering waves.


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  1. Interference and beats 1

  2. Two overlapping waves interfere with each other 2

  3. 11-11 Interference; Principle of Superposition Constructive interference 3

  4. 11-11 Interference; Principle of Superposition Constructive interference Destructive interference 4

  5. 11-11 Interference; Principle of Superposition Constructive interference Destructive interference Somewhere in between 5

  6. Two overlapping waves interfere with each other Constructive interference at C 6

  7. Two overlapping waves interfere with each other Destructive interference at D 7

  8. Interference of Sound Waves: Beats Waves can also interfere in time, causing a phenomenon called beats. Beats are the slow envelope around two waves that are relatively close in frequency. 8

  9. Interference of Sound Waves: Beats Waves can also interfere in time, causing a phenomenon called beats. Beats are the slow envelope around two waves that are relatively close in frequency. Beat frequency = difference in frequency of the two waves 9

  10. Interference of sound waves: Beats https://youtu.be/IQ1q8XvOW6g https://youtu.be/TrpQX5uKxQY 10

  11. Interference of Sound Waves: Beats Waves can also interfere in time, causing a phenomenon called beats. Beats are the slow envelope around two waves that are relatively close in frequency. Beat frequency = difference in frequency of the two waves 11

  12. 12-52: Two piano strings are supposed to be vibrating at 220Hz , but a piano tuner hears three beats every 3.5s when they are played together. If one is known to be vibrating at 220Hz , what must be the frequency of the other? Is there only one answer? 3beats 3.5sec 3 f = = = Hz 0.85714 Hz The beat frequency is 3.5 The other string must vibrate at ( ) 220 0.85714 Hz 220.86 Hz 219.14 Hz or 12

  13. The Doppler effect 13

  14. The Doppler effect occurs when a source of sound moves with respect to an observer A stationary observer hears a firetruck s siren change in pitch as it drives by 14

  15. They detect the same frequency Observer at rest Observer at rest Firetruck at rest 15

  16. They detect the same frequency Observer at rest Observer at rest Firetruck at rest Firetruck moving Detects a lower frequency and longer wavelength Detects a higher frequency and shorter wavelength 16

  17. The same thing happens if the truck is at rest and the observers move Firetruck at rest This person encounters fewer wavefronts per second when moving away from the truck than when standing still This person encounters more wavefronts per second when moving towards the truck than when standing still Therefore measures a lower frequency Therefore measures a higher frequency 17

  18. The Doppler effect Suppose: sound v f is the frequency of the sound emitted by the source as measured when the source and observer are stationary ' f measured by the observer is the frequency and the sound source and/or the observer moves, and: is the speed of sound The frequencies are related as follows sound v v observer v v = ' f f sound source The upper signs apply if the source and observer move CLOSER TOGETHER The lower signs apply if the source and observer MOVE APART 18

  19. iClicker Question Two people are moving closer together. Each will hear the other s voice A with a lower pitch B with a higher pitch C the same as when they were motionless D in a higher amplitude E in a lower amplitude 19

  20. = 343m/s sound v Example 12-15: The siren of a police car at rest emits at a predominant frequency of 1600 Hz. What frequency will you hear if you are at rest and the police car moves at 25 m/s (a) towards you, and (b) away from you? (a) You and the police car are moving closer together: Use the upper signs = 0 observer v + sound v v observer v v f = 1600 Hz = ' f f = 25m/s source v sound source + 343 0 343 25 = = ' 1600 Hz 1726 Hz f ' 1726 Hz f = 20

  21. = 343m/s sound v Example 12-15: The siren of a police car at rest emits at a predominant frequency of 1600 Hz. What frequency will you hear if you are at rest and the police car moves at 25 m/s (a) towards you, and (b) away from you? (b) You and the police car are moving apart: Use the lower signs = 0 observer v sound v v observer v v + f = 1600 Hz = ' f f = 25m/s source v sound source 343 0 343 25 + = = ' 1600 Hz 1491Hz f ' 1491Hz f = 21

  22. = 343m/s sound v Example 12-15: The siren of a police car at rest emits at a predominant frequency of 1600 Hz. What frequency will you hear if you are at rest and the police car moves at 25 m/s (a) towards you, and (b) away from you? So, as the car approaches and moves past you, you hear the siren drop in pitch. Specifically, it goes from to 1726 Hz. 1491Hz 22

  23. 12.57: A bat at rest sends out ultrasonic sound waves at 46.5kHz and receives them returned from an object moving directly away from it at 31.5m/s . What is the received sound frequency? sound v v observer v v = ' f f sound source The upper signs apply if the source and observer move CLOSER TOGETHER The lower signs apply if the source and observer MOVE APART Assume the bat is at rest. The frequency received by the object is = sound v observer v + ' f f 0 sound v Bat Object 343m/sec 31.5m/sec 343m/sec = ' f f f = 46,500 Hz f = ' 42,229.6 Hz 23

  24. 12.57: A bat at rest sends out ultrasonic sound waves at 46.5kHz and receives them returned from an object moving directly away from it at 31.5m/s . What is the received sound frequency? Next, the sound bounces off the moving object and returns to the bat. So now we have a moving source and a stationary observer 24

  25. 12.57: A bat at rest sends out ultrasonic sound waves at 46.5kHz and receives them returned from an object moving directly away from it at 31.5m/s . What is the received sound frequency? sound v v observer v v = ' f f sound source The upper signs apply if the source and observer move CLOSER TOGETHER The lower signs apply if the source and observer MOVE APART Assume the bat is at rest. The frequency received by the bat is = 0 sound v '' ' f f + sound v source v Bat Object 343m/sec = '' ' f f 343m/sec+31.5m/sec f = ' 42,229.6Hz f = '' 38,677.6 Hz 38.7 kHz 25

  26. So, the bat gets information about the object (e.g., an insect): How far away it is (time for the signal to return) Which way it is going and how fast (Doppler shift) 26

  27. Measuring sound reflections is the basis of sonar (sound navigation ranging ) Locate things underwater Geology The method is also used in medical applications in combination with the Doppler effect The emitted and received signal can be mixed and the resulting beats can be measured Example: Monitoring the location, movements, and heartbeat of a fetus 27

  28. Where does the Doppler formula come from? 28

  29. The Doppler effect The source emits wavefronts at frequency f 1. f Wavefronts = T The time between emissions is Source = = sound v f Recall T = . T and therefore sound v 29

  30. The Doppler effect Now suppose that the source moves toward the right with speed source v Source 30

  31. The Doppler effect Now suppose that the source moves toward the right with speed source v In time T, it moves a distance = d source v T d source source ' This shortens the distance between the emitted wavefronts, so that Source = ' d source = ' source v T = ' source v sound v = T Recall that: sound v source v v = ' 1 sound 31

  32. The Doppler effect source v v = ' 1 sound This is the wavelength that would be measured by a stationary observer d The observer would perceive a frequency given by source ' = ' ' sound v f sound v Observer Source = ' f ' 1 v v sound v = ' f 1 source sound f = ' f source v v 1 sound 32

  33. The Doppler effect This is valid when the source moves TOWARDS the observer: sound v v f = ' f source v v d sound 1 source sound ' sound v Observer Source = ' f f sound v source v ' f f Notice: 33

  34. The Doppler effect If the source moves AWAY from the observer, the same argument goes through but with a sign change (go back and check!!): d source sound v + = ' ' f f sound v source v Observer Source ' f f Notice: 34

  35. The Doppler effect We can combine these results: d source ' sound v = ' f f sound v source v Observer Source Source moves toward observer: upper sign Source moves away from observer: lower sign 35

  36. The Doppler effect What if the source is stationary, but the observer moves? Here, the observer moves towards the source. From the observer s perspective, the sound waves move at speed observer v sound v = + ' v sound v observer v Observer Source + ' sound v observer v f v = = ' f Thus the observer detects a frequency / sound v + sound v observer v sound v f = ' f f = = v f sound v 36

  37. The Doppler effect What if the source is stationary, but the observer moves? Here, the observer moves TOWARDS the source. observer v + sound v observer v sound v = ' f f sound v Observer Source 37

  38. The Doppler effect What if the source is stationary, but the observer moves? Here, the observer moves AWAY from the source. observer v sound v observer v sound v = ' f f sound v Observer Source 38

  39. The Doppler effect All these results can be combined into this equation: sound v v observer v v = ' f f sound source The upper signs apply if the source and observer move CLOSER TOGETHER The lower signs apply if the source and observer MOVE APART 39

  40. THE END of Chapter 12 40

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