Waves
•
•
Energy can be transported by
transfer of matter. For example by
a thrown object.
Energy can also be transported by
wave motion without the transfer
of matter. For example by sound
waves and electromagnetic waves.
Waves
•
•
Mechanical waves travel through
matter. The matter is referred to as a
“medium”. Examples are sound eaves,
waves on a string, and waves on water.
Electromagnetic waves do not
require a medium through which to
travel. Examples are gamma rays, xrays, ultraviolet light visible light etc.
Waves
•
A wave is a disturbance or oscillation
that travels through matter or space,
accompanied by a transfer of energy.
Waves
A transverse wave causes the
medium particles to vibrate in
the direction perpendicular to
the motion of the wave.
Waves
A longitudinal wave causes the
medium particles to vibrate in the
direction parallel to the motion of the
wave.
Waves
A pulse is a single disturbance
travelling through a medium or space.
Figure 14-7
A Reflected Wave Pulse: Fixed End
Figure 14-8
A Reflected Wave Pulse: Free End
A crest is the point on a wave with
the maximum value of upward
displacement within a cycle.
A trough is the point on a wave with
the minimum value of downward
displacement within a cycle.
The amplitude is the value of
the maximum or the minimum
displacement from the average
position
The wavelength (l) is the
distance between corresponding
points on consecutive waves.
Unit: m
The frequency (f) is the
number of waves that
pass a given point per
unit time.
-1
Unit: Hz=s
The speed of a wave is
given by
v=fl
Unit: m/s
Figure 14-1
A Wave on a String
Waves
A standing wave oscillates
with time but appears to
be fixed in its location
Figure 14-19
Wave superposition occurs when two or more waves meet
in the same medium. The principle of superposition states
that at the point where two or more waves meet the
displacement of the medium equals the sum of the
displacements of the individual waves.
Figure 14-20
The effect of two or more waves travelling
through a medium is called interference.
Constructive
interference
Destructive
interference
Figure 14-20
Nodes and antinodes
• Nodes occur at points where two waves
interact in such a way that the medium
remains undisturbed.
• Antinodes occur at points where two waves
interact in such a way that maximum
displacement of the medium occurs.
Figure 14-20
Nodes and antinodes
Antinode
Node
Figure 14-20
Nodes and antinodes
• If one end of a string is attached to a vibrating
object, and the other end is fixed, two wave
trains are produced. One by the incident
vibration, and one by reflection from the fixed
end. The reflected wave train returns to the
source and is reflected again. If the second
reflection is in phase with the source,
constructive and destructive interference will
produce stationary antinodes and nodes. The
string will appear to be vibrating in segments.
Figure 14-20
Nodes and antinodes
• This is called a standing wave an is an example
of resonance.
String fixed at both ends
Figure 14-24b
Harmonics
Figure 14-24c
Harmonics
Reflection of Waves
• When a wave train strikes a barrier it is
reflected.
• The law of reflection states that the
angle of incidence is equal to the angle
of reflection.
• The direction of the wave train’s travel
is called a ray, and the angles are
measured from the normal to the
boundary.
Reflection
Refraction of Waves
• When a wave train moves from one
medium to another, its velocity changes.
• Since the waves in the new medium are
produced by the waves in the old
medium, their frequency remains the
same. Since the velocity changes, but
not the frequency, the wavelength must
change.
Refraction of Waves
• When parallel waves approach a
boundary between media along the
normal, their direction does not change.
• When parallel waves approach a
boundary between media at an angle to
the normal, their direction is changed.
This phenomenon is called refraction.
Refraction of Waves
• When parallel waves approach a
boundary between media along the
normal, their direction does not change.
• When parallel waves approach a
boundary between media at an angle to
the normal, their direction is changed.
This phenomenon is called refraction.
Refraction of Waves
Boundary
Refraction of Waves
Boundary
Diffraction of Waves
• Diffraction is the bending of waves
around obstacles in their path.
Diffraction of Waves
Diffraction of Waves
Diffraction of Waves
• An interference pattern can be
created by placing a barrier with two
openings in front of a wave train.
• The openings must be smaller than
the wavelength of the approaching
wave train.
Diffraction of Waves
• In regions where crests overlap with
crests, and troughs overlap with troughs,
constructive interference occurs, and
antinodes lie along those lines. These
lines are called antinodal lines.
• In regions where crests overlap with
troughs destructive interference occurs,
and the medium is undisturbed. These
lines are called nodal lines.
Diffraction of Waves
• The pattern produced is called an
interference pattern.
• Different wavelengths produce similar
interference patterns, but the nodal and
antinodal lines are in different places.
• Regardless of wavelength a central
antinodal line always falls in the center
of the pattern.
Standing waves on a string –
In order for standing waves to
form on a string, the length of the
string L must be a multiple of one
half the wavelength
Ln
l
2
n  1, 2,3...
String fixed at both ends
l  2L
Figure 14-24b
Harmonics
lL
Figure 14-24c
Harmonics
2
l L
3
Speed of waves on a string
v=
F

mass
=
length
F  the tension in the string
Speed of waves on a string
Example
A 4.0 m length of string has a mass of 20.00g. It is stretced between two points,
and experiences a tension of 40.0N. The string is plucked.
a) What is the velocity of a wave on the string?
b)What is the longest wavelength possible
for a standing wave on the string?
c) What is the frequency of the longest wavelength possible
for a standing wave on the string?
Speed of waves on a string
Solution
mass 0.02000kg
3 kg
a)  =

 5.00 10
length
4.0m
m
v=
F

=
40.0 N
m
=89.44
s
3 kg
5.00 10
m
Speed of waves on a string
Solution
b)Longest wavelength possible is l =2L
l =2  4.0m  8.0m
m
88.44
v
s  11.055Hz
c )v  f l  f  
l
8.0m