4.2 Travelling Waves
4.2 Travelling Waves
© Kari Eloranta
2017
Jyväskylän Lyseon lukio
International Baccalaureate
January 17, 2017
© Kari Eloranta 2017
4.2 Travelling Waves
4.2 Travelling Waves
Introduction
Wave Sources
Figure: When a stick is dipped into the water, a series of circular disturbances are created (©
Roger McLassus).
© Kari Eloranta 2017
4.2 Travelling Waves
4.2 Travelling Waves
Introduction
Wave Sources
A periodic oscillator can act as a
wave source.
If the end of a rope is connected
to an oscillator (such as a
moving hand), continuous pulses
travel on the rope forming a
wave.
Oscillating electrons create
electromagnetic waves in
antennae.
Human vocal cords, and musical Figure: Vibrating air colums in musical instruments
instruments, create sound waves. create sound waves (© Infrogmation).
© Kari Eloranta 2017
4.2 Travelling Waves
4.2 Travelling Waves
Introduction
Travelling Waves
Wave Pulse
Wave pulse is a travelling disturbance in a medium.
Travelling Wave
Travelling wave is a series of travelling wave pulses.
Examples of travelling waves include water waves, sound waves, and
electromagnetic waves.
Water and sound waves are examples of mechanical travelling waves, where
disturbations travel in a medium.
Electromagnetic waves do not need a medium in which to travel. The speed
of electromagnetic waves in vacuum is c = 3.00 × 108 ms−1.
© Kari Eloranta 2017
4.2 Travelling Waves
4.2 Travelling Waves
Basic Concepts
Amplitude A of a Wave
Amplitude
Amplitude is the greatest distance from the equilibrium position.
cm x
4
3
2
1
−1
−2
−3
x = A, amplitude = A
0.5
1.0
1.5
t
s
x = −A, amplitude = A
Figure: Double arrows show the times when displacement from the equilibrium position x = 0 is
greatest (displacement = amplitude, that is, x = A ). Because amplitude is the magnitude of
displacement, it is always positive.
© Kari Eloranta 2017
4.2 Travelling Waves
4.2 Travelling Waves
Basic Concepts
Period T of a Wave
Definition of Period T
Period T of a travelling wave is the time taken by the wave to travel one
wavelength.
0.75
Period T = 0.60s
0.25
0.50
Period is T = 0.60s
Period T = 0.60s
−1
−2
−3
Period T = 0.60s
cm x
4
3
2
1
1.00
1.25
1.50
1.75
Figure: The period can be measured from any two points on a graph that correspond to one
wavelength. Here we have used two successive crests.
© Kari Eloranta 2017
4.2 Travelling Waves
t
s
4.2 Travelling Waves
Basic Concepts
Frequency f
Definition of Frequency of Wave f
Frequency of a wave f is the number of full wave lengths per unit time.
Frequency f
The frequency is
1
f =
T
where T is the period of a wave.
The unit of frequency is
1
1
[f ] =
= = 1Hz
[T ] s
For example, the frequency of a tuning fork is 400 Hz, or the frequency of
visible light is from 400 Hz to 800 Hz.
© Kari Eloranta 2017
4.2 Travelling Waves
(1)
4.2 Travelling Waves
Basic Concepts
Wavelength λ
cm
y
0.30
0.20
0.10
−0.10
−0.20
−0.30
wavelength λ
x
0.5
1.0
1.5
2.0
2.5
3.0
cm
Wavelength
Wavelength is the shortest distance along the wave between two points in phase
with one another (OR: distance travelled by the wave in one period).
© Kari Eloranta 2017
4.2 Travelling Waves
4.2 Travelling Waves
Basic Concepts
Amplitude A
cm
y
0.30
0.20
0.10
−0.10
−0.20
−0.30
amplitude A = 0.30m
x
0.5
1.0
1.5
2.0
2.5
3.0
amplitude A = 0.30m
Amplitude
Amplitude is the greatest displacement from the equilibrium position.
In the figure above, the amplitude is A = 0.30m from the x -axis.
© Kari Eloranta 2017
4.2 Travelling Waves
cm
4.2 Travelling Waves
Basic Concepts
Period T
cm
y
0.30
0.20
0.10
−0.10
−0.20
−0.30
period T
t
0.5
1.0
1.5
2.0
2.5
3.0
s
Period T
Period is the time taken for one complete oscillation (OR: time taken for one cycle
to pass a given point).
© Kari Eloranta 2017
4.2 Travelling Waves
4.2 Travelling Waves
Basic Concepts
Wave Equation
Wave Equation
The speed of the travelling wave is
λ
v = λf =
T
(2)
where λ is the wavelength, f the frequency, and T the period of the wave.
The speed of a wave gives the speed of the energy transfer in a travelling wave.
For mechanical waves the speed depends on the medium and its temperature.
The speed of the electromagnetic waves depends also on the medium.
Typical wave speeds include the speed of sound in air 340 ms−1, the speed of
sound in water 1480 ms−1, and the speed of light in vacuum (air)
c = 2.998 × 108 ms−1.
© Kari Eloranta 2017
4.2 Travelling Waves
4.2 Travelling Waves
Basic Concepts
Mechanical Longitudinal Wave
Mechanical Longitudinal Wave
A longitudinal wave is a wave in which the direction of motion of the energy
transfer is parallel to the direction of motion of the particles of the medium.
Sound waves are an example of mechanical longitudinal waves.
Longitudinal waves can travel in all types of medium: gas, liquid and solid.
© Kari Eloranta 2017
4.2 Travelling Waves
4.2 Travelling Waves
Basic Concepts
Mechanical Transverse Wave
Mechanical Transverse Wave
Transverse wave is a wave in which the direction of motion of the energy transfer
is perpendicular to the direction of motion of the particles of the medium.
Traveling pulses in a rope, or S-type Earth quake waves are examples of
mechanical transverse waves.
Mechanical transverse waves cannot exist in gases, because there are no
intermolecular forces that could produce such motion.
Electromagnetic waves are non-mechanical transverse waves, in which the
electric field oscillates at right angles to the direction of the wave.
© Kari Eloranta 2017
4.2 Travelling Waves