CH14_Zinke3e_PLS_PPT.ppt----------------

PowerPoint
Presentations for
Physics for the
Life Sciences
Adapted for the
Third Edition by
Philip Backman
University of
New Brunswick
Copyright © 2017 by Nelson Education Ltd.

Waves
Chapter 14

KEY POINT
A wave is the propagation of disturbance in
a medium in space and time.
Thus, a wave is a pattern that moves along
the medium, but there is no net motion of
the medium along with the wave.
14-3

KEY POINT
The direction of oscillation of a particle and
the direction of the propagating wave are
perpendicular for transverse waves and
parallel for longitudinal waves.
14-4

14-5

14-6

Concept Question
Why is it important to keep quiet and not make
an impulsive sound such as a gunshot in
avalanche country?
14-7

Concept Question
Which one of the following statements is false?
(a) A wave can have both transverse and
longitudinal components.
(b) A wave carries energy from one place to
another.
(c) A wave does not result in the flow of the
material of its medium.
(d) A wave is a travelling disturbance.
(e) A transverse wave is one in which the
disturbance is parallel to the direction of travel.
14-8

The speed of a wave is equal to the product of
its wavelength (l) and frequency (ƒ).
Wave Speed
f
T
v l
l


wave
T
f
1

where
14-9

Example
What is the wavelength of a wave whose speed
is 75.0 m/s and frequency is 200 Hz?
The frequency and the speed of the wave
are known.
m
375
.
0
Hz
200
s
m
0
.
75
wave
wave 




f
v
f
v l
l
14-10

KEY POINTS
The maximum distance of a point on a wave
measured from the equilibrium position is
the amplitude.
The period T is the amount of time it takes for
a point on the wave to go through one complete
cycle of oscillation.
14-11

KEY POINTS
The frequency, ƒ, is the number of complete
cycles of a wave that pass a given point per unit
time. It is the number of oscillations per unit time
in the wave.
The speed of a wave is equal to the product of its
wavelength and frequency.
14-12

14-13

The Wave Function
)
(
)
,
( vt
x
f
t
x
y 

The displacement depends on both the position x
and time t, and may be written as y(x, t).
14-14

14-15

14-16

1
2
1
2
wave
t
t
x
x
t
x
v






Phase Velocity
14-17

The speed of a wave on a string, a stretched
rope, or a Slinky is computed using the tension
(T), or the force that is exerted to keep it
stretched, and the linear mass density (m),
or the mass per unit length of the string or rope.
m
T
v 
14-18

Example
A uniform cord of length 6.00 m and mass 30.0 g
is stretched by a force of 20 N. Find the speed of
a wave travelling along the cord.
First calculate the linear mass density of the cord:
m
kg
10
00
.
5
m
00
.
6
kg
10
0
.
30 3
3







l
m
m
14-19

Example (continued)
s
m
2
.
63
m
kg
10
00
.
5
N
0
.
20
3





m
T
v
The speed of the travelling wave:
14-20

Concept Question
If a string with length L and tension T is cut in
half but is wound to the same tension, how will
the speed of a wave on it be affected?
(a) The speed of wave on the string increases
by a factor of .
(b) The speed of wave on the string decreases
by a factor of .
2
2
(continued)
14-21

Concept Question (continued)
(c) The speed of wave on the string decreases
by a factor of 2.
(d) The speed of wave on the string stays the
same, unchanged.
(e) Without knowing the mass of the string,
it is impossible to say.
14-22

Harmonic Waves














 ft
x
A
t
x
y 
l

2
sin
)
,
(
Harmonic waves are caused by harmonic
vibrations. Harmonic vibrations are those that
have sinusoidal functions.
A is the amplitude, ƒ the frequency, and λ the
wavelength.
14-23

Harmonic Waves
 
t
kx
A
t
x
y 

sin
)
,
( 
Where: f

 2

l

2

k
And notice:
k
T
v

l


14-24

14-25

14-26

Concept Question
What is the amplitude of the wave shown on
the next slide?
(a) 3 m
(b) 6 m
(c) 1.5 m
(d) 4.0 m
(e) need more information
14-27

14-28

Concept Question
What is the period of the wave shown on the
next slide?
(a) 3 s
(b) 6 s
(c) 1.5 s
(d) 4.0 s
(e) need more information
14-29

14-30

KEY POINT
Principle of superposition: If two or more
travelling waves overlap, the resultant disturbance
(wave) is the sum of the disturbances of the
individual waves.
14-31

14-32

KEY POINTS
When the phase difference between two harmonic
waves is an even integer (multiples) of , the
interference is constructive.
When the phase difference is an odd integer of ,
the interference is destructive. When the phase
difference is between these two cases, the
interference is neither fully constructive nor fully
destructive, and it is said to be intermediate.
14-33

14-34

14-35

14-36

14-37

Standing Waves
A standing wave is a wave pattern that is fixed
in space and does not move.
Standing waves are produced in a medium either
because the medium is moving in the opposite
direction with respect to the wave, or because
two identical waves, with the same wavelength
and the same amplitude, moving in opposite
directions are interfering with one another in a
stationary medium.
14-38

14-39

The wave function of a standing wave:
  )
cos(
sin
)
,
( t
kx
A
t
x
y 

14-40

14-41

14-42

14-43

Concept Question
A standing wave on a long string has antinodes at
Points 4 cm, 8 cm, 12 cm, and 16 cm.
What are the wavelengths of the travelling waves
that produce this standing wave?
(a) 0.78 cm
(b) 2 cm
(c) 4 cm
(d) 8 cm
(e) 12.6 cm
14-44

14-45

For a string of length L, with both ends fixed,
resonant frequencies are given by:
.
.
.
.
3,
2,
1,
n
for
2


L
v
n
fn
14-46

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