Today: waves
Exam Results, HW4 reminder
• Exam: Class average = 13.6/20 ( at B/BC boundary)
– Exam scores posted this afternoon on Learn@UW
– Exam solutions are on course web page
• Have talked about Newton’s laws, motion of
particles, momentum, energy, etc.
• Basically a description of things that move.
• Waves are a different type of object
– They move (propagate), but in a different way
• March Chap 7: Question A, Exercises 2
Griffith Chap 15: Q5, Q9, E4, E10
• Due Wed. Feb. 15
Friday, Feb. 10
Phy107 Lecture 10
• Examples:
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Waves on a rope
Sound waves
Water waves
Stadium wave!
Friday, Feb. 10
Chapter 8: Wave Motion
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What is moving?
• A wave is a sort of motion
– But unlike motion of particles
• Mechanical waves require:
• A propagating disturbance
– 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 rope stays in one place
– The disturbance moves down the rope
• The disturbance in the medium moves through the
medium.
• Energy moves down the rope.
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Motion of a piece of the rope
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Energy transport
• Moving rope sections have some energy of motion (kinetic).
• If rope section is not moving, kinetic energy is zero.
• Determine motion by looking at rope position at two different
times.
• As the wave passes through, a piece of the
rope vibrates up and down.
Zero
velocity
As the pulse passes, there is kinetic energy
of motion.
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Zero
velocity
Time=1.0 sec
Time=1.1
5
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Positive and negative
velocities
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1
Question
How does the wave travel
Kinetic energy (1/2)mass x (velocity)2
is transported down rope as wave pulse moves.
Suppose the rope gradually tapers along its length.
The wave pulse
• Energy is transmitted down the rope
• Each little segment of rope at position x
has some mass m(x),
and moves at a velocity v(x),
1
and has kinetic energy m(x)v(x) 2
A. speeds up
B. slows down
C. keeps same speed
2
!
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Wave on a whip
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.
Numerical solutions of a realistic whip
(a) Initial loop
(b) whip when the tip reaches the fastest velocity
(c) whip at time t=0.02 s
Whip tapers from handle to tip, so
that wave velocity increases.
‘Crack’ occurs as tip breaks sound barrier!
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Wave on a towel
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How does the pulse propagate?
• Towel tip breaks sound
barrier on a good crack
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2
Wave speed
Question
Two ropes of different mass/length. On which
does the pulse propagate fastest?
• The speed of sound is higher in solids than in gases
– The molecules in a solid interact more strongly,
elastic property larger
A. Heavier rope
• The speed is slower in liquids than in solids
B. Lighter rope
– Liquids are softer, elastic property smaller
• Speed of waves on a string
C. Both the same
Tension
Mass per unit length
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• 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
• 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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Magical waves
Waves can reflect
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Some wave properties
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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
1) Energy transfer along the direction of
propagation.
2) Speed is characteristic of the medium
elastic properties and inertia (mass) density
3) obey the principle of superposition - two
superposed disturbances add or subtract
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Longitudinal Waves
Graph of longitudinal wave
• 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
• A longitudinal wave can also be
represented as a graph
• Compressions correspond to crests and
stretches correspond to troughs
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Producing a Sound Wave
Sound waves
• Sound waves are longitudinal 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
• 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
– Mass density of the air (mass per unit volume)
– and the ‘compressibility’ of the air
– Area of compression
• Tine swings to left
– Area of rarefaction
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Sound from a Tuning Fork
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Continuous wave
• Can generate a wave that occupies all of the
rope by continuing to shake the end up and
down.
• 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
Friday, Feb.rarefactions
10
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• 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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4
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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