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### It is a pulse Interference What happens when waves overlap or touch Interference Can be Constructive crest ... Sound Waves Plan changes Key points Sound ... – PowerPoint PPT presentation

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Title: Waves

1
Waves
• April 19, 2010

2
What do you know?
• Name all the different types of waves you can
think of
• What does a wave do?
• Or why does nature need waves?
• Consider the result if there were no waves
• Think of the Dec 26, 2004 Tsunami

3
Hookes Law
• The force of a spring changes
• Depending on how far you stretch it
• Turns out F -ks
• If a mass is hanging off a spring
• SF ma
• At rest Fs W ma 0

4
Boing
• A mass of 2.4 kg is suspended from a spring.
• The weight stretches the spring 0.13 m.
• Determine the spring constant for the spring.

5
• AKA Simple Harmonic Motion
• SHM
• For example
• Springs
• Pendulum

6
Periodic Motion
• What makes it so?
• Back and forth along the same path.
• Position, speed and acceleration
• All repeat on same cycle
• Spring
• When is it at max speed?
• When is it at max acceleration?
• Pendulum?

7
Describing Periodic Motion
• Frequency (f)
• Number of cycles per unit time
• 1/seconds Hz
• Period (T)
• Time to go through a complete cycle
• Seconds
• T 1/f
• A pendulum goes through 5 cycles in 10 seconds.
• What is its period?
• Its frequency?

8
Pendulums Period - Galileo figured it out
• Mass has nothing to do with it
• Just like free fall!!
• The amplitude doesnt affect it either!
• It does depend on L
• T 2p(L/g)½
• What is the period for a pendulum with a length
of 1.8 meters?

9
Quick Recap
• What is frequency?
• What is period?
• How long of string would give you a period of 1
second?
• T 2p(L/g)½
• L 0.25 meters

10
The nature of waves
• Imagine a buoy on the ocean
• What happens to it as waves go by?

11
Why waves?
• The stuff stays put
• Waves carry energy from place to place

12
Wave Properties
• Crest Top of Wave
• Trough Bottom of Wave
• Wavelength length for one cycle
• Amplitude versus wave height?

13
Speed
• Measured in meters per second.
• v wave length x frequency
• Or
• V ? f
• Speed is constant for a given medium

14
For a spring
• Period is related to a couple things
• Any ideas?

15
Spring Lab
• Does the period of a spring depend on
• The distance stretched?
• The k value?
• 3 springs
• Find k
• Measure ?s
• Then 3 trials each
• Different stretches
• Use the same mass

16
Waves
• April 21, 2010

17
Homework
• 441
• 3) 2700 N/m
• 4) 81 N
• 449
• 140 m
• 0.25 m
• 3.6 m
• 451
• 210 N/m
• 25 N/m

18
Lab T of springs
• What affected the period?
• T 2p(m/k)½
• How close does your data fit?

19
Waves
• Two types of waves
• Mechanical
• Electromagnetic
• Mechanical
• Require a medium
• Like air, or water, or string, or spring
• Electromagnetic
• They are special no medium required

20
Mechanical Waves
• Two types of mechanical waves
• Transverse
• Longitudinal
• What is the difference?
• Transverse wiggles perpendicular (across)
• Longitudinal wiggles along the wave direction

21
Transverse Waves
• Classic sinusoidal wave
• Crest
• Trough
• Wavelength
• Amplitude

22
Longitudinal Waves
• Pressure wave
• Sections of
• compression
• rarefaction (stretch)
• Sound is a longitudinal wave

23
Wave Speed
• Velocity wavelength x frequency
• V ?f
• (Distance of 1 cycle) / (time for 1 cycle)
• Speed of a mechanical wave is constant for any
given medium
• Wise up other my mixed words would be.

24
Example
• Piano middle C has a frequency of 264 Hz
• The velocity of sound in air is 343 m/s
• What is the wavelength of the middle C?
• V ?f
• ? v/f
• 343 m/s / 264 Hz 1.30 meters

25
Does it repeat?
• If it does
• It is a periodic wave
• If not
• It is a pulse

26
Interference
• What happens when waves overlap or touch

27
Interference
• Can be Constructive
• crest lines up with another resulting in adding
effect
• More or less energy?

28
Interference
• Or can be Destructive
• Crest overlaps a trough resulting in reducing
effect.
• Smaller amplitude

29
USCGC Ironwood
30
Reflection
• If you send a pulse through a medium and it
strikes a barrier
• What do you think happens to the wave?
• It depends

31
Standing waves
• They are the result of interference
• Nodes and antinodes

32
• Pulses
• Periodic waves
• Standing waves
• Nodes
• Spread out around the room

33
Mechanical Waves
• April 23, 2010

34
In the southern seas

35
Today
• Notes on Waves
• Sound
• Doppler
• Lab A day at the beach

36
Sound waves
• Sound waves are compression waves
• Longitudinal waves
• Move out in a 3-D sphere
• We hear certain frequencies
• 20 20,000 Hz
• Different animalsdifferent frequencies
• Dogs, elephants, frogs

37
Sound wave properties
• Amplitude
• How loud the sound is
• Related to its energy
• Frequency and wavelength
• The pitch (how high or low the note is)
• Generally speaking
• Speed is greater through solids than liquids
• And liquids faster than in air

38
Doppler Effect
• Sound from a stationary object goes out in all
directions
• A spherical wave
• Produces a ripple

39
Doppler
• What happens when you move the object?
• It gets closer to the wave that just left
• The space between the waves decreases
• Wavelength gets smaller

40
Doppler v ?f still applies
• If the wavelength gets smaller
• The frequency must get bigger
• Remember
• Velocity wavelength x frequency

41
Hmmm
• If you ran towards a car
• Would you get the same effect?

42
Break the sound barrier
43
Lab at the beach!
• Explores the relationship between depth of water
and the speed of waves
• What do you think????
• Consider what weve learned about Interference
Doppler (not part of lab)

44
Sound Waves
• April 27, 2010

45
Plan changes
• Survey monkey says
• Lab makeup time today
• Lesson will stretch over

46
Key points
• Intensity
• Forced Vibrations and Resonance
• Beats

47
Sound intensity
• Tied to amplitude of the waves
• Intensity
• The amount of power per unit area
• I P/A (Watts per meter2)
• For a spherical wave (like sound)
• I P/4pr2
• This is the wave intensity of sound at some
distance r from the source!

48
Intensity
• Note the relationship
• I P/4pr2
• As distance increases
• The intensity changes by the inverse square
• Units are Watts/m2

49
Our ears are logarithmic
• If you double the intensity of a sound
• We perceive a slight increase in loudness
• In order to double the loudness the intensity
must increase 10 times!
• We developed a scale that lets us manage this
easier
• The decibel scale

50
Decibels (dB)
• The relative intensity
• Relates the intensity to our hearing threshold
• 0 dB cant hear it
• 50 dB normal conversation
• 70 dB vacuum cleaner
• 90 dB lawn mower
• 120 dB pain threshold
• Note that this is NOT the frequency
• But is the LOUDNESS!

51
Decibel Scale
• The difference between 100 and 110 decibels
• Results in a doubling of effective loudness
• Is 10 times more intensity

52
Hmmm
• What do
• the Tacoma Narrows Bridge and
• an opera singer breaking a wine glass with their
voice
• have in common?

53
Resonance
• All things have a natural vibration frequency
• When an object vibrates
• It tends to cause other items to vibrate
• Same natural frequency?
• Resonance occurs

54
Lab make-up time
• Or Resonance Video

55
Lab
• Speed of a tsunami
• v (gh)1/2
• In water of depth 4 km, you can verify that the
tsunami speed is about 200 m/s or 400 mph.

56
Harmonics
• April 29, 2010

57
Today
es/MovieCailleron.html
• Notes on Harmonics
• Review Sheet
• Lab Resonance

58
Key points
• Resonance and beats
• Standing sound waves
• Strings Pipes

59
Beats
• When the frequencies are just a bit off
• You hear pulses or beats
• Systematic wave interference
• Constructive and
• Destructive

60
of Beats
• How can you determine the number of beats (per
second)?
• Subtract the frequencies
• We can generally only distinguish about 10 beats
after that we just hear a different pitch

61
Harmonics of a string
• Ends of the string are not moving
• They must be nodes
• Longest wavelength possible
• Is the twice the length of the string
• Which give you the lowest frequency
• AKA the fundamental frequency

62
Next possible standing wave
• 3 nodes second harmonic
• Wavelength cut in half
• Frequency doubled
• 4 nodes third harmonic
• Fundamental wavelength/3
• Frequency tripled
• etcetera

63
Vibrating air columns
• Open ends represent antinodes
• Both ends open?
• Longest wave length equals twice the column
height
• One end closed?
• Longest wave length equals
• Four times the column height
• Only odd harmonics are present in a closed pipe

64
What do harmonics do for us?
• They allow a rich variety of sound
• Why my voice sounds different that yours
• Why a trumpet doesnt sound like a guitar
• Each sound has its own mixture of harmonics
• That add together through superposition
• Provide a sound quality we call timbre

65
Consider this waveform
• Combine 2 waves
• Wavelength of 1 meter
• And 2 meters

66
Resonance Lab
• A nice way to see the effects of REZ

67
Wave Goodbye
• May 3, 2010

68
Review
• Periodic motion
• Simple Harmonic Motion (SHM)
• Pendulum and springs
• Waves types and properties
• Electromagnetic and
• Mechanical
• Compression and longitudinal

69
Waves
• Wave speed
• v f?
• For a given medium
• Speed generally increases with density
• Wave speed and depth
• http//www.yenka.com/freecontent/item.action?quick
15h

70
Tsunami
• Speed of a tsunami increases with depth
• v (gh)1/2
• In water of depth 4 km, you can verify that the
tsunami speed is about 200 m/s or 400 mph.

71
Waves
• Doppler
• Sound barrier
• Interference
• Resonance and Natural Frequency

72
Harmonics
• Draw standing waves for harmonic series
• Use v f? to determine speed, frequency, etc.

73
Explore sound
• Be able to explain what you see here!

74
For the twirling tone tubes
• How do you make the frequency higher?
• What is at play? Sketch the harmonics

75
For the xylophone
• What difference does the size/shape make?

76