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Chapter 15
Wave Motion
Dr. Armen Kocharian
Lecture 3 and 4
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Goals for Chapter 15 To study the properties and varieties of mechanical waves
To relate the speed, frequency, and wavelength of
periodic waves
To interpret periodic waves mathematically
To calculate the speed of a wave on a string
To calculate the energy of mechanical waves
To understand the interference of mechanical waves
To analyze standing waves on a string
To investigate the sound produced by stringed
instruments
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Types of mechanical waves
A mechanical wave is a disturbance traveling through a medium.
Figure below illustrates transverse waves and longitudinal waves.
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Longitudinal waves
a. Longitudinal waves (sound in air)
b. Longitudinal waves (spring vibrations)
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Transverse waves
a. Transverse waves (sound in air)
b. Longitudinal waves (spring vibrations)
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Periodic waves
For a periodic wave, each particle of the medium undergoes periodic motion.
The wavelength of a periodic wave is the length of one complete wave pattern.
The speed of any periodic wave of frequency f is v = f.
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Periodic transverse waves For the transverse waves
shown here in Figures 15.3 and 15.4, the particles move up and down, but the wave moves to the right.
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Periodic longitudinal waves For the longitudinal waves
shown here in Figures 15.6 and 15.7, the particles oscillate back and forth along the same direction that the wave moves.
Follow Example 15.1.
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Mathematical description of a wave
The wave function, y(x,t), gives a
mathematical description of a
wave. In this function, y is the
displacement of a particle at time
t and position x.
The wave function for a
sinusoidal wave moving in the +x-
direction is y(x,t) = Acos(kx t), where k = 2/ is called the wave number.
Figure 15.8 at the right illustrates
a sinusoidal wave.
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Types of Waves
There are two main types of waves
Mechanical waves
Some physical medium is being disturbed
The wave is the propagation of a disturbance through a
medium
Electromagnetic waves
No medium required
Examples are light, radio waves, x-rays
Matter waves
Quantum mechanics
Particle propagation
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General Features of Waves
In wave motion, energy is transferred over a
distance
Matter is not transferred over a distance
All waves carry energy
The amount of energy and the mechanism
responsible for the transport of the energy differ
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Mechanical Wave
Requirements
Some source of disturbance
A medium that can be disturbed
Some physical mechanism through which
elements of the medium can influence each
other
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Pulse on a String
The wave is generated by a flick on one end of the string
The string is under tension
A single bump is formed and travels along the string The bump is called a
pulse
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Pulse on a String
The string is the medium through which the pulse travels
The pulse has a definite height
The pulse has a definite speed of propagation along the medium
The shape of the pulse changes very little as it travels along the string
A continuous flicking of the string would produce a periodic disturbance which would form a sinusoidal type wave
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Transverse Wave
A traveling wave or pulse
that causes the elements of
the disturbed medium to
move perpendicular to the
direction of propagation is
called a transverse wave
The particle motion is
shown by the blue arrow
The direction of propagation
is shown by the red arrow
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Longitudinal Wave
A traveling wave or pulse that causes the elements of the disturbed medium to move parallel to the direction of propagation is called a longitudinal wave
The displacement of the coils is parallel to the propagation
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Complex Waves
Some waves exhibit a combination of transverse
and longitudinal waves
Surface water waves are an example
Use the active figure to observe the displacements
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Complex Waves
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Example: Earthquake Waves
P waves P stands for primary
Fastest, at 7 8 km / s
Longitudinal
S waves S stands for secondary
Slower, at 4 5 km/s
Transverse
A seismograph records the waves and allows determination of information about the earthquakes place of origin
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Traveling Pulse
The shape of the pulse at t = 0 is shown
The shape can be represented by
y (x,0) = f (x) This describes the
transverse position y of the element of the string located at each value of x at t = 0
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Traveling Pulse, 2
The speed of the pulse is v
At some time, t, the pulse
has traveled a distance vt
The shape of the pulse
does not change
Its position is now
y = f (x vt)
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Traveling Pulse, 3
For a pulse traveling to the right y (x, t) = f (x vt)
For a pulse traveling to the left y (x, t) = f (x + vt)
The function y is also called the wave function:
y (x, t)
The wave function represents the y coordinate of any element located at position x at any time t The y coordinate is the transverse position
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Traveling Pulse, final
If t is fixed (snapshot) then the wave function
as a function of position is called the
waveform
It defines a curve representing the actual
geometric shape of the pulse at that time
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Sinusoidal Waves
The wave represented by
the curve shown is a
sinusoidal wave
It is the same curve as sin q plotted against q
This is the simplest
example of a periodic
continuous wave
It can be used to build more
complex waves
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Sinusoidal Waves, cont
The wave moves toward the right In the previous example, the brown wave represents the
initial position
As the wave moves toward the right, it will eventually be at the position of the blue curve
Each element moves up and down in simple harmonic motion
It is important to distinguish between the motion of the wave and the motion of the particles of the medium
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Wave Model
The wave model is a new simplification
model
Allows to explore more analysis models for
solving problems
An ideal wave has a single frequency
An ideal wave is infinitely long
Ideal waves can be combined
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Terminology: Amplitude and
Wavelength
The crest of the wave is the location of the maximum displacement of the element from its normal position This distance is called
the amplitude, A
The wavelength, , is the distance from one crest to the next
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Terminology: Wavelength and
Period
More generally, the wavelength is the
minimum distance between any two identical
points on adjacent waves
The period, T , is the time interval required for
two identical points of adjacent waves to pass
by a point
The period of the wave is the same as the period
of the simple harmonic oscillation of one element
of the medium
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Terminology: Frequency
The frequency, , is the number of crests (or any point on the wave) that pass a given
point in a unit time interval
The time interval is most commonly the second
The frequency of the wave is the same as the
frequency of the simple harmonic motion of one
element of the medium
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Terminology: Frequency, cont
The frequency and the period are related
When the time interval is the second, the
units of frequency are s-1 = Hz
Hz is a hertz
1
T
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Terminology, Example
The wavelength, , is 40.0 cm
The amplitude, A, is
15.0 cm
The wave function can
be written in the form y
= A cos(kx t)
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Speed of Waves
Waves travel with a specific speed
The speed depends on the properties of the medium being disturbed
The wave function is given by
This is for a wave moving to the right
For a wave moving to the left, replace x vt
with x + vt
2( , ) cosy x t A x vt
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Wave Function, Another Form
Since speed is distance divided by time,
v = / T
The wave function can then be expressed as
This form shows the periodic nature of y
y can be used as shorthand notation for y(x, t)
( , ) cos 2
x ty x t A
T
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Wave Equations
We can also define the angular wave number
(or just wave number), k
The angular frequency can also be defined
2k
22
T
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Sinusoidal Wave on a String
To create a series of pulses, the string can be attached to an oscillating blade
The wave consists of a series of identical waveforms
The relationships between speed, velocity, and period hold
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Sinusoidal Wave on a String, 2
Each element of the string
oscillates vertically with
simple harmonic motion
For example, point P
Every element of the string
can be treated as a simple
harmonic oscillator vibrating
with a frequency equal to
the frequency of the
oscillation of the blade
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Sinusoidal Wave on a String, 3
The transverse speed
of the element is
or vy = A SIN(kx t)
This is different than
the speed of the wave
itself
constant
y
x
dyv
dt
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Sinusoidal Wave on a String, 4
The transverse
acceleration of the
element is
or ay = 2A COS(kx t)
constant
y
y
x
dva
dt
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Sinusoidal Wave on a String, 5
The maximum values of the transverse speed
and transverse acceleration are
vy, max = A
ay, max = 2A
The transverse speed and acceleration do
not reach their maximum values
simultaneously
v is a maximum at y = 0
a is a maximum at y = A
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The Linear Wave Equation
The wave functions y (x, t) represent solutions of an
equation called the linear wave equation
This equation gives a complete description of the
wave motion
From it you can determine the wave speed
The linear wave equation is basic to many forms of
wave motion
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Linear Wave Equation, General
The equation can be written as
2 2
2 2 2
1y y
x v t
, cosy x t A kx t
2
2 2
2
,, cos ,y
y x ta x t A kx t y x t
t
Wave function
Velocity,
,, siny
y x tv x t A kx t
t
Acceleration,
The second derivative is,
22 2
2cos ,
yk A kx t k y x t
x
2 2 2
2 2 2
y k y
x t
v
k
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Linear Wave Equation, General
The equation can be written as
This applies in general to various types of traveling waves y represents various positions
For a string, it is the vertical displacement of the elements of the string
For a sound wave, it is the longitudinal position of the elements from the equilibrium position
For em waves, it is the electric or magnetic field components
2 2
2 2 2
1y y
x v t
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Linear Wave Equation, General
cont
The linear wave equation is satisfied by any
wave function having the form
y = f (x vt)
The linear wave equation is also a direct
consequence of Newtons Second Law applied to any element of a string carrying a
traveling wave
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Example 15.1 and 15.2
15.1
15.2
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Graphing the wave function
The graphs in Figure 15.9 a
and b to the right look similar,
but they are not identical.
Graph (a) shows the shape of
the string at t = 0, but graph
(b) shows the displacement y
as a function of time at t = 0.
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Particle velocity and acceleration in a sinusoidal
wave The graphs below show the velocity and acceleration
of particles of a string carrying a transverse wave.
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The speed of a wave on a string
q
1 tany Ax
F y
F x
q
2 tany Bx x
F y
F x
1 2y y y
x x x
y yF F F F
x x
The net y component of force q q (tan tan )y B AF F
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The speed of a wave on a string
.Fv
2
2y
x x x
y y yF F x
x x t
The Newton Law:
2
2y y
yF ma x
t
Dividing both sides by Fx
2
2x x x
y y
yx x
x F t
2 2
2 2
y y
x F t
0x
2 22
2 2
y yv
x twave equation
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Calculating wave speed
Follow Example 15.3 and refer to Figure 15.14 below.
220.0 9.8 / 196boxF m g kg m s N
2.000.0250 /
80.0
ropem kgkg m
L m
The ropes linear density is
The waves speed is
19688.5 /
0.0250 /
F Nv m s
kg m
The wavelength is
1
88.5 /44.3
2,00
v m sm
f s
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Energy in a wave motion
A wave transfers power along a string because it transfers
energy.
The average power is equal:
,,y
y x tF x t F
x
, ( , ) ,y yP x t F x t v x t
where
,,y
y x tv x t
t
, cosy x t A kx t For sinusoidal wave,
,sin
y x tkA kx t
x
,sin
y x tA kx t
t
2 2, sinP x t Fk A kx t
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Energy in a wave motion, cont
By using relationships vk
Average Power
2 2 2 2 2 2, sin sinF
P x t A kx t F A kx tv
2 /v F
2 2, sinP x t Fk A kx t
2max, sinP x t P kx t
2 2maxP F A
Power is reduced to
where
2 2 maxmax max, sin sin2
PP x t P kx t P kx t
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Useful relationships
2 2
2 2
2 2
1
2
1
2
1
2
P A v
FP A
P A F
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Power in a wave
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Wave intensity
The intensity of a wave is the
average power it carries per unit
area.
If the waves spread out uniformly in
all directions and no energy is
absorbed, the intensity I at any
distance r from a wave source is
inversely proportional to r2: I 1/r2.
1 2
14
PI
r 2 2
24
PI
r 2 21 1 2 24 4r I r I
2
1 22
2 1
I r
I r
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Wave intensity: Example 15.5
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Boundary conditions
When a wave
reflects from a fixed
end, the pulse
inverts as it reflects.
See Figure
15.19(a) at the
right.
When a wave
reflects from a free
end, the pulse
reflects without
inverting. See
Figure 15.19(b) at
the right.
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Reflection of Pulse on
a String
Reflection from a HARD boundary
Propagation of pulse
Reflection from a
SOFT boundary
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Wave interference and
superposition
Interference is the
result of overlapping
waves.
Principle of super-
position: When two
or more pulses
(waves) overlap, the
total displacement is
the sum of the
displacements of the
individual pulses
(waves).
1 2, , ,y x t y x t y x t
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Wave interference and
superposition
Interference is the
result of overlapping
pulses (waves).
Principle of super-
position: When two
or more waves
overlap, the total
displacement is the
sum of the displace-
ments of the
individual pulses
(waves).
1 2, , ,y x t y x t y x t
Two pulses with different
shapes
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Wave interference and
superposition
Interference is the
result of overlapping
waves.
Principle of super-
position: When two
or more waves
overlap, the total
displacement is the
sum of the displace-
ments of the
individual waves.
1 2, , ,y x t y x t y x t
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Standing waves on a String
Interference is the result of overlapping waves.
Principle of super-position: When two or more waves
overlap, the total displacement is the sum of the
displacements of the individual waves
1 , cosy x t A kx t
Incident wave traveling to the left
Reflected wave traveling to the right
2 , cosy x t A kx t
Standing wave
1 2, , , cos cosy x t y x t y x t A kx t kx t
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Standing waves on a String
Use relationship
Standing wave is equal to
Standing wave amplitude 2SWA A
Nodes of standing wave is defined
1 2, , , 2 sin siny x t y x t y x t A kx t
cos cos cos sin sina b a b a b
, 0 2 siny x t A kx
This implies, that positions of zero amplitudes or nodes at
sin 0 ,2
n nkx x
k 0,1,2,3,...n
The positions of antinodes at
3... , 1,3,5,...
4 4 4
nx n
1 2, , , cos cosy x t y x t y x t A kx t kx t
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Standing waves on a String
The diagrams above show standing-wave patterns produced at various
times by two waves of equal amplitude traveling in opposite directions.
In a standing wave, the elements of the medium alternate between the
extremes shown in (a) and (c).
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Standing waves on a String
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Standing waves on a string
The distance between adjacent antinodes is /2. The distance between adjacent nodes is /2. The distance between a node and an adjacent antinode is /4
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Standing waves on a string Waves traveling in opposite directions on a taut
string interfere with each other.
The result is a standing wave pattern that does
not move on the string.
Destructive interference occurs where the wave
displacements cancel, and constructive
interference occurs where the displacements add.
At the nodes no motion occurs, and at the
antinodes the amplitude of the motion is greatest.
Figure below shows several standing wave
patterns.
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The formation of a standing wave
A wave to the left
combines with a
wave to the right
to form a standing
wave.
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Example 15.6 Standing wave on a guitar string
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Normal modes of a string
For a taut string fixed at
both ends, the possible
wavelengths are n = 2L/n and the possible frequencies
are fn = n v/2L = nf1, where
n = 1, 2, 3,
f1 - is the minimal
fundamental frequency,
f2 - is the second harmonic
(first overtone),
f3 is the third harmonic
(second overtone), etc.
Right figure illustrates the
first four harmonics.
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Standing waves and musical
instruments
A stringed instrument is tuned to the correct frequency
(pitch) by varying the tension. Longer strings produce bass
notes and shorter strings produce treble notes. (See Figure
below.)
.
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Example 15.7
2n
n Ff
L 1
1
2
Ff
L 2 214F L f
1 1,2,32
n
vf n nf n
L
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Example 15.8
n nv f
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Speed of a Wave on a String
The speed of the wave depends on the physical characteristics of the string and the tension to which the string is subjected
Restoring force (tension, T) and inertia (mass per unit length, )
This assumes that the tension is not affected by the pulse
This does not assume any particular shape for the pulse
tension
mass/length
Tv
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Resonance on a String
Because an oscillating system exhibits a large amplitude when driven at any of its
natural frequencies, these frequencies are referred to as resonance frequencies.
If the system is driven at a frequency that is not one of the natural frequencies, the
oscillations are of low amplitude and exhibit no stable pattern
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Speed of a Wave on a String
Tv
v f
One end of the string is attached to a vibrating blade f. The other end passes over a pulley with a hanging mass attached to the end. This produces the tension in the string and increase of speed v. The string is vibrating in its second harmonic, with larger .
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Reflection of a Wave, Fixed
End
When the pulse
reaches the support,
the pulse moves back
along the string in the
opposite direction
This is the reflection of
the pulse
The pulse is inverted
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Reflection of a Wave, Free End
With a free end, the
string is free to move
vertically
The pulse is reflected
The pulse is not
inverted
The reflected pulse has
the same amplitude as
the initial pulse
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Transmission of a Wave
When the boundary is
intermediate between
the last two extremes
Part of the energy in
the incident pulse is
reflected and part
undergoes transmission
Some energy
passes through the
boundary
Similar to fixed end.
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Transmission of a Wave, 2
Assume a light string is attached to a heavier string
The pulse travels through the light string and reaches the boundary
The part of the pulse that is reflected is inverted
The reflected pulse has a smaller amplitude
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Transmission of a Wave, 3
Assume a heavier
string is attached to a
light string
Part of the pulse is
reflected and part is
transmitted
The reflected part is not
inverted
Similar to free end.
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Transmission of Pulse on
a String
Propagation of pulse from light to heavy string
Propagation of wave from
heavy to light string
a) How do the amplitudes of the reflected and transmitted waves compare to the
amplitude of the incident wave?
b) How do the widths of the reflected and transmitted waves compare to the width of
the incident wave?
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Transmission of a Wave, 4
Conservation of energy governs the pulse When a pulse is broken up into reflected and transmitted
parts at a boundary, the sum of the energies of the two pulses must equal the energy of the original pulse
When a wave or pulse travels from medium A to medium B and vA > vB, it is inverted upon reflection B is denser than A
When a wave or pulse travels from medium A to medium B and vA < vB, it is not inverted upon reflection A is denser than B
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Introduction Earthquake waves
carry enormous power as they travel through the earth.
Other types of mechanical waves, such as sound waves or the vibration of the strings of a piano, carry far less energy.
Overlapping waves interfere, which helps us understand musical instruments.
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Conceptual
Checkpoints
Chapter 15
Waves
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If you double the wavelength of a wave on a string, what happens to
the wave speed v and the wave frequency f?
A. v is doubled and f is doubled.
B. v is doubled and f is unchanged.
C. v is unchanged and f is halved.
D. v is unchanged and f is doubled.
E. v is halved and f is unchanged.
Q15.1
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If you double the wavelength of a wave on a string, what happens to
the wave speed v and the wave frequency f?
A. v is doubled and f is doubled.
B. v is doubled and f is unchanged.
C. v is unchanged and f is halved.
D. v is unchanged and f is doubled.
E. v is halved and f is unchanged.
A15.1
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Which of the following wave functions describe a wave that moves in
the x-direction?
A. y(x,t) = A sin (kx t)
B. y(x,t) = A sin (kx + t)
C. y(x,t) = A cos (kx + t)
D. both B. and C.
E. all of A., B., and C.
Q15.2
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Which of the following wave functions describe a wave that moves in
the x-direction?
A. y(x,t) = A sin (kx t)
B. y(x,t) = A sin (kx + t)
C. y(x,t) = A cos (kx + t)
D. both B. and C.
E. all of A., B., and C.
A15.2
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A wave on a string is moving to the right. This
graph of y(x, t) versus coordinate x for a specific
time t shows the shape of part of the string at that
time.
At this time, what is the velocity of a particle of the
string at x = a?
A. The velocity is upward.
B. The velocity is downward.
C. The velocity is zero.
D. not enough information given to decide
Q15.3
x
y
0 a
-
A wave on a string is moving to the right. This
graph of y(x, t) versus coordinate x for a specific
time t shows the shape of part of the string at that
time.
At this time, what is the velocity of a particle of the
string at x = a?
A. The velocity is upward.
B. The velocity is downward.
C. The velocity is zero.
D. not enough information given to decide
A15.3
x
y
0 a
-
A wave on a string is moving to the right. This
graph of y(x, t) versus coordinate x for a specific
time t shows the shape of part of the string at that
time.
At this time, what is the acceleration of a particle of
the string at x = a?
A. The acceleration is upward.
B. The acceleration is downward.
C. The acceleration is zero.
D. not enough information given to decide
Q15.4
x
y
0 a
-
A wave on a string is moving to the right. This
graph of y(x, t) versus coordinate x for a specific
time t shows the shape of part of the string at that
time.
At this time, what is the acceleration of a particle of
the string at x = a?
A. The acceleration is upward.
B. The acceleration is downward.
C. The acceleration is zero.
D. not enough information given to decide
A15.4
x
y
0 a
-
A wave on a string is moving to the right. This
graph of y(x, t) versus coordinate x for a specific
time t shows the shape of part of the string at that
time.
At this time, what is the velocity of a particle of the
string at x = b?
A. The velocity is upward.
B. The velocity is downward.
C. The velocity is zero.
D. not enough information given to decide
Q15.5
x
y
0 b
-
A wave on a string is moving to the right. This
graph of y(x, t) versus coordinate x for a specific
time t shows the shape of part of the string at that
time.
At this time, what is the velocity of a particle of the
string at x = b?
A. The velocity is upward.
B. The velocity is downward.
C. The velocity is zero.
D. not enough information given to decide
A15.5
x
y
0 b
-
A wave on a string is moving to the right. This
graph of y(x, t) versus coordinate x for a specific
time t shows the shape of part of the string at that
time.
A. only one of points 1, 2, 3, 4, 5, and 6.
B. point 1 and point 4 only.
C. point 2 and point 6 only.
D. point 3 and point 5 only.
E. three or more of points 1, 2, 3, 4, 5, and 6.
Q15.6
At this time, the velocity of a particle on the string is upward at
-
A wave on a string is moving to the right. This
graph of y(x, t) versus coordinate x for a specific
time t shows the shape of part of the string at that
time.
A. only one of points 1, 2, 3, 4, 5, and 6.
B. point 1 and point 4 only.
C. point 2 and point 6 only.
D. point 3 and point 5 only.
E. three or more of points 1, 2, 3, 4, 5, and 6.
A15.6
At this time, the velocity of a particle on the string is upward at
-
A. 4 times the wavelength of the wave on string #1.
B. twice the wavelength of the wave on string #1.
C. the same as the wavelength of the wave on string #1.
D. 1/2 of the wavelength of the wave on string #1.
E. 1/4 of the wavelength of the wave on string #1.
Q15.7
Two identical strings are each under the same tension. Each string has a
sinusoidal wave with the same average power Pav.
If the wave on string #2 has twice the amplitude of the wave on string #1, the
wavelength of the wave on string #2 must be
-
Two identical strings are each under the same tension. Each string has a
sinusoidal wave with the same average power Pav.
If the wave on string #2 has twice the amplitude of the wave on string #1, the
wavelength of the wave on string #2 must be
A. 4 times the wavelength of the wave on string #1.
B. twice the wavelength of the wave on string #1.
C. the same as the wavelength of the wave on string #1.
D. 1/2 of the wavelength of the wave on string #1.
E. 1/4 of the wavelength of the wave on string #1.
A15.7
-
The four strings of a musical instrument are all made of the same material and
are under the same tension, but have different thicknesses. Waves travel
A. fastest on the thickest string.
B. fastest on the thinnest string.
C. at the same speed on all strings.
D. not enough information given to decide
Q15.8
-
The four strings of a musical instrument are all made of the same material and
are under the same tension, but have different thicknesses. Waves travel
A. fastest on the thickest string.
B. fastest on the thinnest string.
C. at the same speed on all strings.
D. not enough information given to decide
A15.8
-
While a guitar string is vibrating, you gently touch the midpoint of the
string to ensure that the string does not vibrate at that point.
The lowest-frequency standing wave that could be present on the
string
A. vibrates at the fundamental frequency.
B. vibrates at twice the fundamental frequency.
C. vibrates at 3 times the fundamental frequency.
D. vibrates at 4 times the fundamental frequency.
E. not enough information given to decide
Q15.9
-
While a guitar string is vibrating, you gently touch the midpoint of the
string to ensure that the string does not vibrate at that point.
The lowest-frequency standing wave that could be present on the
string
A. vibrates at the fundamental frequency.
B. vibrates at twice the fundamental frequency.
C. vibrates at 3 times the fundamental frequency.
D. vibrates at 4 times the fundamental frequency.
E. not enough information given to decide
A15.9
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The graph at the top is the history graph at x = 4 m of a
wave traveling to the right at a speed of 2 m/s. Which is
the history graph of this wave at x = 0 m?
(1) (2) (3) (4)
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The graph at the top is the history graph at x = 4 m of a
wave traveling to the right at a speed of 2 m/s. Which is
the history graph of this wave at x = 0 m?
(3) (4) (1) (2)
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Which of the following actions would make a pulse travel
faster down a stretched string?
1. Move your hand up and down more quickly as you
generate the pulse.
2. Move your hand up and down a larger distance as
you generate the pulse.
3. Use a heavier string of the same length, under the
same tension.
4. Use a lighter string of the same length, under the
same tension.
5. Use a longer string of the same thickness, density
and tension.
-
Which of the following actions would make a pulse travel
faster down a stretched string?
1. Move your hand up and down more quickly as you
generate the pulse.
2. Move your hand up and down a larger distance as
you generate the pulse.
3. Use a heavier string of the same length, under the
same tension.
4. Use a lighter string of the same length, under the
same tension.
5. Use a longer string of the same thickness, density
and tension.
-
What is the frequency of this
traveling wave?
1. 10 Hz
2. 5 Hz
3. 2 Hz
4. 0.2 Hz
5. 0.1 Hz
-
What is the frequency of this
traveling wave?
1. 10 Hz
2. 5 Hz
3. 2 Hz
4. 0.2 Hz
5. 0.1 Hz
-
What is the phase difference between the crest of a
wave and the adjacent trough?
1. 0
2. /4
3. /2
4. 3 /2
5.
-
What is the phase difference between the crest of a
wave and the adjacent trough?
1. 0
2. /4
3. /2
4. 3 /2
5.
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A graph showing wave displacement versus position at a
specific instant of time is called a
1. snapshot graph.
2. history graph.
3. bar graph.
4. line graph.
5. composite graph.
-
A graph showing wave displacement versus position at a
specific instant of time is called a
1. snapshot graph.
2. history graph.
3. bar graph.
4. line graph.
5. composite graph.
-
A graph showing wave displacement versus time at a
specific point in space is called a
1. snapshot graph.
2. history graph.
3. bar graph.
4. line graph.
5. composite graph.
-
A graph showing wave displacement versus time at a
specific point in space is called a
1. snapshot graph.
2. history graph.
3. bar graph.
4. line graph.
5. composite graph.
-
A wave front diagram shows
1. the wavelengths of a wave.
2. the crests of a wave.
3. how the wave looks as it moves toward
you.
4. the forces acting on a string thats under
tension.
5. Wave front diagrams were not discussed in
this chapter.
-
A wave front diagram shows
1. the wavelengths of a wave.
2. the crests of a wave.
3. how the wave looks as it moves toward
you.
4. the forces acting on a string thats under
tension.
5. Wave front diagrams were not discussed in
this chapter.
-
The waves analyzed in this chapter are
1. sound waves.
2. light waves.
3. string waves.
4. water waves.
5. all of the above.
-
The waves analyzed in this chapter are
1. sound waves.
2. light waves.
3. string waves.
4. water waves.
5. all of the above.
-
Introduction Earthquake waves
carry enormous power as they travel through the earth.
Other types of mechanical waves, such as sound waves or the vibration of the strings of a piano, carry far less energy.
Overlapping waves interfere, which helps us understand musical instruments.