phy107 fall 06 1 exam results exam: –exam scores posted on learn@uw no homework due next week d c...
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Phy107 Fall 06 1
Exam Results
• Exam: – Exam scores posted on Learn@UW
• No homework due next week
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Phy107 Fall 06 2
Today: waves
• Have studied Newton’s laws, motion of particles, momentum, energy, etc.
• Laws for describing things that move.
• Waves are a different type of object– They move (propagate), but in a different way
• Examples:– Waves on a rope– Sound waves– Water waves– Stadium wave!
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Phy107 Fall 06 3
Wave Motion
• A wave is a type of motion– But unlike motion of particles
• A propagating disturbance– The rope stays in one place– The disturbance moves down the rope
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Phy107 Fall 06 4
What is moving?• Mechanical waves require:
– Some source of disturbance– A medium that can be disturbed– Some physical connection between or mechanism though which adjacent portions of the medium influence each other
– Waves move at a velocity determined by the medium
• The disturbance in the medium moves through the medium.
• Energy moves down the rope.
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Phy107 Fall 06 5
Motion of a piece of the rope
• As the wave passes through, a piece of the rope vibrates up and down.
As the pulse passes, there is kinetic energy of motion.
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Phy107 Fall 06 6
Energy transport
Time=1.0 secTime=1.1 sec
Zero velocity
Zero velocity
Positive and negative velocities
• If rope section is not moving, kinetic energy is zero.
• Determine motion by looking at rope position at two different times.
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Phy107 Fall 06 7
How does the wave travel
• Energy is transmitted down the rope
• Each little segment of rope at position xhas some mass m(x), and moves at a velocity v(x),
and has kinetic energy €
1
2m(x)v(x)2
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Phy107 Fall 06 8
Waves on a whip
The forward crack• The loop travels at velocity c,
whereas a material point on top of the loop moves at velocity 2c.
Whip tapers from handle to tip, so that wave velocity increases.
‘Crack’ occurs as tip breaks sound barrier!
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Phy107 Fall 06 9
Wave speed• The speed of sound is higher in solids than in gases– The molecules in a solid interact more strongly, elastic property larger
• The speed is slower in liquids than in solids– Liquids are softer, elastic property smaller
• Speed of waves on a string
Tension
Mass per unit length
€
v =F
μ€
velocity =elastic _ property
inertial_ property
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Phy107 Fall 06 10
Waves can reflect
• Whenever a traveling wave reaches a boundary, some or all of the wave is reflected
• Like a particle, it bounces back. But…
• When it is reflected from a fixed end, the wave is inverted
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Phy107 Fall 06 11
Superposition of waves
• Two pulses are traveling in opposite directions
• The net displacement when they overlap is the sum of the displacements of the pulses
• Note that the pulses are unchanged after the passing through each other
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Phy107 Fall 06 12
Types of waves
• Wave on a rope was a transverse wave• Transverse wave: each piece of the medium moves perpendicular to the wave propagation direction
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Phy107 Fall 06 13
Longitudinal Waves
• In a longitudinal wave, the elements of the medium undergo displacements parallel to the motion of the wave
• A longitudinal wave is also called a compression wave
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Phy107 Fall 06 14
Graph of longitudinal wave
• A longitudinal wave can also be represented as a graph
• Compressions correspond to crests and stretches correspond to troughs
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Phy107 Fall 06 15
Sound waves
• The medium transporting the wave is the air
• The air is locally compressed, then compresses air next to it, etc.
• The sound velocity depends on– Mass density of the air (mass per unit volume)
– and the ‘compressibility’ of the air
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Phy107 Fall 06 16
Producing a Sound Wave• Sound waves are longitudinal waves traveling through a medium• A tuning fork can be used as an example of producing a sound wave
• As the tines vibrate, they disturb the air near them
• As the tine swings to the right, it forces the air molecules near it closer together
• This produces a high density area in the air– Area of compression
• Tine swings to left– Area of rarefaction
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Phy107 Fall 06 17
Sound from a Tuning Fork
• As the tuning fork continues to vibrate, a succession of compressions and rarefactions spread out from the fork
• A sinusoidal curve can be used to represent the longitudinal wave– Crests correspond to compressions and troughs to rarefactions
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Phy107 Fall 06 18
Continuous wave
• Can generate a wave that occupies all of the rope by continuing to shake the end up and down.
• This wave is present throughout the length of the rope, but also continually moves.
• Can think of a wave source continually emitting waves along the string.
• This is sort of like a string of pulses
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Phy107 Fall 06 19
Waveform – A Picture of a Wave
• Just like the pulse, a continuous wave moves.
• The red curve is a “snapshot” of the wave at some instant in time
• The blue curve is later in time
• A is a crest of the wave
• B is a trough of the wave
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Phy107 Fall 06 20
Description of a Wave
• Amplitude is the maximum displacement of string above the equilibrium position
• Wavelength, , is the distance between two successive points that behave identically
Amplitude
• For instance, the distance between two crests
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Phy107 Fall 06 21
Period, frequency and velocity of a wave
• Period: time required to complete one cycle– Unit = seconds
• Frequency = 1/Period = rate at which cycles are completed – Units are cycles/sec = Hertz
• Period wavelength and velocity are related– If the wave travels one wavelength in the time of one period then
• velocity = wavelength/period
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Phy107 Fall 06 22
Equation form
• Velocity = Wavelength / Period
• v = / T, or v = f
• f = Frequency = 1 / Period = 1/T
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Phy107 Fall 06 23
Periodic waves
• Shake one end of a string up and down with period T (frequency f=1/T). The height (up or down) is the amplitude.
• Peaks move at speed v so are separated by distance (wavelength) =vT = v/f.
• The wave can shake a fixed object with that frequency.
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Phy107 Fall 06 24
Examples
• The speed of sound in air is 340 m/s.
• A source period of 1 Hz=1/s produces a wavelength of =v/f= 340 m
• A string vibrating at frequency f= 340 Hz produces a wavelength =v/f = 1 m
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Phy107 Fall 06 25
Question• A sound wave is traveling through air when in
encounters a large helium-filled balloon. The sound velocity inside the balloon is greater than in the air. Compare the wavelength of the sound wave inside and outside the balloon.
A. inside= outside
B. inside> outside
C. inside< outside
0 1
= v / fThe frequency inside the balloon is the same as outside. Use = v / f to find that the wavelength is less
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Phy107 Fall 06 26
Wave quantities summary
o Time of one COMPLETE up and down motion– one period T = 1/f– one wavelength in one period
o Velocity of disturbance (wave or phase) velocityo Particles don’t move with v (only up-and-down)
or (back and forth)
v = f• v depends only on properties of “medium”
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Phy107 Fall 06 27
Water waves?• Water waves occur on the surface. They are a kind of transverse wave.
On Earth On the sun
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
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Phy107 Fall 06 28
Surface water waves
• Surface water waves produced by wind.
• The wave travels with some speed, but the water does not!
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Phy107 Fall 06 29
Water’s Motion IThe wave travels while the water circles!
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Phy107 Fall 06 30
Water’s Motion• Circling strongest at surface• Weak ~ 1/2 wavelength deep