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Waves

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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
Waves start with periodic motion
  • 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
Slinky Lab
  • Read the lab carefully!
  • Several exercises with slinkies
  • Pulses
  • Periodic waves
  • Standing waves
  • Nodes
  • Spread out around the room

33
Mechanical Waves
  • April 23, 2010

34
In the southern seas
  • Heading into the ice

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
  • Sand waves http//www.lps.ens.fr/douady/SongofDun
    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
Make your own banjo
  • What difference does the size and tightness of
    the rubber band make?

77
Bottleswhat is vibrating air or water?
  • And how does it affect the pitch?
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