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Compiled by: A. Olivier
Published by:
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Fax: 086 596 1071
Email: [email protected]
Grade 12 Physical Sciences Theory and
Workbook Book 2 (Chemistry) consists
of two parts. Part 1 consists of Organic
Chemistry where part 2 consists of
Energy Involved with Chemical Reactions,
Rate of Chemical Reactions, Chemical
Equilibrium, Electrochemistry and Acids
and Bases.
CONTENTS
Topic 1
WAVES, SOUND AND LIGHT
Chapter
1
TRANSVERSE PULSES
Transverse Pulses In A String Or Spring
Superposition Of Pulses
Chapter
2
TRANSVERSE WAVES
Transverse Waves
Chapter
3
12
LONGITUDINAL WAVES
Longitudinal Waves In A Rope Or Spring
Chapter
4
5
22
SOUND
Sound Waves
Chapter
1
5
28
ELECTROMAGNETIC RADIATION
The Nature Of Electromagnetic Radiation
52
Topic 2
ELECTRICITY AND MAGNETISM
Chapter
1
MAGNETISM
Magnetic Fields, Magnetic Poles And Forces
Chapter
2
ELECTROSTATICS
Static Electricity
Chapter
3
69
82
ELECTRIC CIRCUITS
Circuits
Potential Difference And Emf
Current
Resistance
Resistors In Series And Parallel
Click on a page number
105
108
116
124
132
Topic 3
MECHANICS
Chapter
1
VECTORS AND SCALARS
Introduction To Vectors And Scalars
Chapter
2
MOTION IN ONE DIMENSION
Position, Displacement And Distance
Speed And Velocity
Acceleration
Chapter
3
4
169
177
195
VELOCITY AND THE EQUATION OF MOTION
Description Of Motion In Words And Diagrams
Description Of Motion With Graphs
Description Of Motion In Equations Of Motion
The Motion Of A Vehicle And Safety
Chapter
160
198
199
237
247
ENERGY
Gravitational Potential Energy And Kinetic Energy
Conservation Of Mechanical Energy
Click on a page number
251
256
1 TRANSVERSE PULSES
Chapter
TRANSVERSE PULSES IN A STRING OR SPRING
G
PULSES
:KHQWKHPRYHPHQWRIZDYHVDUHVWXGLHGLWLVHDVLHUWR¿UVWLQYHVWLJDWH
the movement of a single pulse, and to describe the characteristics of a
wave later.
The substance or the material along which the pulse moves is called a
medium. The medium carries the pulse from one place to another. The
medium does not create the pulse and is in itself not a pulse. Thus the
medium does not move with the pulse as it moves through the medium.
The particles that form in the medium, temporarily move away from their
rest position. Thus water is a medium for a water wave. We use a spring
and/or rope as a medium to study transverse pulses and waves.
Figure 1 A slinky (spiral), helix spring (weak
spring) or a heavy rope can be used to study
waves.
Slinky
Helix spring
Figure 2 below shows a single pulse that moves along a rope (as medium).
Heavy rope
Movement of pulse
Figure
Figu
g re 2 A pulse m
moves
o es a
ov
along
long a rope
A person that holds the one end of a rope, makes an up-down movement with her hand. Such a single non-recurring
disturbance is called a p
pulse. It causes a disturbance that moves along
g the rope.
p
A pulse is a single disturbance in a medium (spring or rope) that moves
from one point to another.
The pulse is created
by th
the source (h
(hand)
down th
the rope, b
butt th
the rope d
does nott move with. The particles
t db
d) and
d moves d
in the rope (or coils of a spring) move perpendicular to the direction the pulse moves in. This pulse is called a
transverse pulse.
A transverse pulse occurs when the particles of the medium move
perpendicular with the propagation direction of the medium.
The propagation direction of a pulse is the direction in which the pulse moves along the rope (or spring).
amplitude
displacement
pulse length
y
x
distance
pulse speed
disturbance or displacement
RISDUWLFOHVǻy)
position of rest
equilibrium
Figure 4 Pulse terminology
Figure 3 shows a few words that are used to describe a transverse pulse:
‡ Rest position (equilibrium): This is the position of the rope or spring when no pulse or disturbance moves
through it.
‡ Amplitude: The maximum displacement (maximum disturbance) of a particle in a medium from its
position of rest (equilibrium) is called the amplitude of the pulse.
‡ Pulse length: Is the distance from the starting point of the pulse to the end point of the pulse.
‡ A pulse thus has an amplitude, pulse length and pulse speed but no frequency (repetition per second),
because a pulse is only a single disturbance.
‡ We call the pulse in one direction relative to the rest position (equilibrium) a peak and the pulse in the
other direction a trough (or valley). A peak is some times referred to as a positive pulse and a trough a
negative pulse.
WAVES, SOUND AND LIGHT
1
‡ Pulse speed: Is the distance that the pulse travels per time.
_
If the pulse moves a distance D in a time t, the speed is v: v = D
t
Not all pulses are transverse. There are also other types of pulses called longitudinal pulses. Longitudinal pulses
causes the particles to move in a direction parallel to the propagation direction.
Example
1
A pulse moves 4 m in 8 s in a heavy rope. Calculate the speed of the pulse.
Solution
D = 4 m; t = 8 s; v = ? m.s-1
_
v=D
t
___
m
=4
= 0,8 m.s-1
Practical Activity
1
Generation of transverse pulses
Method:
+ROGWKHVSLUDOVSULQJRQWKHZRUNÀRRUDVVKRZQLQ)LJXUH
‡ spiral spring or strong rope
2. Have a friend hold the other end of the spring tightly (or attach it to an object
‡ small piece of string or ribbon
that will not move) Mark point (A) with a small piece of string on the spring.
To view the PHET pulse in a rope 3. Pull the free end of the spring and quickly move it to one side and back to its
simulation, visit:
original position to generate a pulse. (A pulse is only one movement of the spring).
sp
phet.colorado.edu/sims
A
Choose waves and then waves on
string.
WHAT YOU NEED
Figure 5 Demonstration of a transverse pulse with the aid of a spiral spri
spring.
Questions
1. Graphically represent the pulse that moves down in the spring. In your diagram, clearly show in which
direction the movement of the pulse is and in which direction the displacement is from the average position.
2. In which direction did the pulse travel? _________________________________________________________
3. In which direction is the disturbance? __________________________________________________________
4. What happens at A? _______________________________________________________________________
_______________________________________________________________________________________
)RUPXODWH D GH¿QLWLRQ RI D WUDQVYHUVH SXOVH BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
________________________________________________________________________________________
2
TOPIC 1
Exersise 1
TRANSVERSE PULSES IN A ROPE OR SPRING
'H¿QHHDFKRIWKHIROORZLQJWHUPVUHJDUGLQJDWUDQVYHUVHSXOVH
$SXOVHBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
7UDQVYHUVHSXOVHBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
______________________________________________________________________________________
$PSOLWXGHBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
__________________________________________________________________________________________
3XOVHOHQJWKBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
3XOVHVSHHGBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
2. Liza uses a spiral spring to generate a transverse pulse.
2.1 How must Liza move her hand to generate a transverse
pulse?
______________________________________________
2.2 How do the coils compare to the direction that the pulse
moves in?
Figure 6 A transverse pulse on a slinky spring.
______________________________________________________________________________________
2.3 Explain how the motion of the coils allows the pulse to propagate.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
2.4 Draw a sketch of the transverse pulse and show the pulse length, amplitude and rest position.
$SXOVHPRYHVPLQV&DOFXODWHWKH
VSHHGRIWKHSXOVH
$SXOVHKDVDVSHHGRIFP.s-1. How
IDUGRHVLWPRYHLQV"
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
WAVES, SOUND AND LIGHT
3
$SXOVHKDVDVSHHGRIP.s-1. How
ORQJGRHVLWWDNHWRPRYHDGLVWDQFHRI
P"
3.4 How long will it take for a pulse that moves
P.s-1 to move a distance of 20 m?
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
________________________________
4. A domestic worker wants to shake the dust from a rug by generating a pulse.
P
Q
rug
coin
3m
4.1 Describe how the pulse is generated in the rug.
_____________________________________________________________________________________
_____________________________________________________________________________________
__________________________________________________________________________________________
4.2 What type of pulse is generated in the rug? ___________________________________________________
4.3 What is the direction of the motion of P and Q at that moment (write only resting, moving upwards or
moving downwards).
3BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
4 BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB
A coin on the furthermost end of the rug is brought into motion after 2 s.
([SODLQLIWKHFRLQLVVKDNHQRIIWKHUXJRUQRW
4.4 Calculate the speed of the pulse.
________________________________
_____________________________________________
________________________________
_____________________________________________
________________________________
_____________________________________________
7KHGLDJUDPVKRZVWZRSXOVHVLQWKHVDPHPHGLXP:KLFKRQHKDVWKHKLJKHUVSHHG"([SODLQ
B
A
__________________________________________________________________________________________
__________________________________________________________________________________________
4
TOPIC 1
SUPERPOSITION OF PULSES
SUPERPOSITION
$VLPSOHH[SHULPHQWZLWKDKHOLFDOVSULQJRUVWURQJURSHHQDEOHVXVWR¿QGRXWKRZSXOVHVLQÀXHQFHHDFKRWKHU
when they pass each other. Figure 8, 9 and 10 shows the effect.
Figure 8 A transverse pulse is generated
from both ends of a spiral spring.
Figure 9 The two pulses cross
each other.
Figure 10
After the two pulses
cross each other, they move further
unchanged.
Careful observation shows that:
‡WKHWZRSXOVHVPRYHLQGHSHQGHQWO\RIHDFKRWKHU
‡ZKHQWKH\FURVVWKHWZRSXOVHVXQLWHVRWKDWWKHDPSOLWXGHRIWKHGLVWXUEDQFHDWWKHSRLQWRIFURVVLQJLVPXFK
bigger as that of any of the other original pulses.
‡DIWHUWKHFURVVLQJWKHWZRSXOVHVWDNHRQWKHLURULJLQDOIRUPDQGFRQWLQXHGXQFKDQJHGDVLIQRWKLQJKDSSHQHG each in its particular direction.
The phenomenon is called superposition of pulses. The Principle of Superposition states that:
When two pulses meet simultaneously at the same point in a medium, the instantaneous displacement
at the point is the algebraic sum of the displacements of each pulse at that moment.
This effect (result) that the two pulses have on each other when they are superimposed, is known as interference
Interference occurs when two or more pulses (or waves) interrelate in the same space, at the same time
Two types off interference
are di
distinguished,
and
T
i
f
i
i h d namely
l constructive
i iinterference
f
d destructive
d
i iinterference.
f
CONSTRUCTIVE INTERFERENCE
Constructive interference occurs when two pulses meet on the same side of the rope (the same side as the
rest position). They strengthen each other to form a higher pulse. i.e. with a larger amplitude. After constructive
interference the two pulses (with the original amplitudes) continue in their original direction of motion.
a+b
b
a
a
b
b
a
Figure 11 Superposition of two pulses on the same side of the equilibrium position = constructive interference.
DESTRUCTIVE INTERFERENCE
Destructive interference occurs when two pulses that are on the opposite sides of the rope (the opposite sides
of the position of rest) meet. They weaken each other to form a smaller pulse, i.e. with a smaller amplitude, or even
causing no pulse for a moment. After destructive interference the two pulses (with their original amplitude) continue
in their original direction of motion.
b
b
a+b
a
a
Figure 12 Superposition of two pulses on the opposite sides of the equilibrium position = destructive interference.
Example
2
Calculate the amplitude of the combined pulses when two
SXOVHVRQDURSHDSSURDFKHDFKRWKHUDVIROORZV
(1)
(2)
140 mm
WAVES, SOUND AND LIGHT
140 mm
50 mm
5
Solution
7KHDPSOLWXGHVRIWKHWZRSXOVHVDUHUHVSHFWLYHO\PPDQGPP
&RPELQHGDPSOLWXGH PPPP PPDERYHWKHUHVWSRVLWLRQ
7KHDPSOLWXGHVRIWKHWZRSXOVHVDUHUHVSHFWLYHO\PPDQGPP
7KHFRPELQHGDPSOLWXGH PPPP PPDERYHWKHUHVWSRVLWLRQ
Practical Activity
WHAT YOU NEED
‡ wave tank
‡ water
‡ 2 rulers
2
Observe constructive and destructive interference
Method:
6HWXSDZDYHWDQN)LOOWKHZDYHWDQNZLWKZDWHUWRDGHSWKDSSUR[LPDWHO\
10 mm.
)RUPWZRVXUIDFHSXOVHVE\
placing two rulers simultaneously
in the water and observe what
happens when the pulses
cross and after they have
crossed.
)RUPWZRVXUIDFHSXOVHVE\SODFLQJWZRUXOHUVLQWKHZDWHUDWGLIIHUHQW
times. And observe what happens when the pulses cross and after they
have crossed.
)RUPDVXUIDFHSXOVHE\ placing a ruler in the water.
Figure 13 A Wave tank
Questions
1. The following diagram shows how the pulses that are formed simultaneously in the water moves towards
HDFKRWKHU:KDWLVREVHUYHGZKHQWKHSXOVHVFURVVDQGDIWHUWKH\KDYHFURVVHG"&RQ¿UP\RXUDQVZHU
by drawing two pulses that move towards each other and then moves away from each other.
______________________________________________________________________________
_______________________________________________________________________________
___________________________________________________________________________________
2. The following diagram shows how pulses that are formed at different times in the water move toward each
RWKHU:KDWLVREVHUYHGZKHQWKHSXOVHVFURVVDQGDIWHUWKH\KDYHFURVVHG"&RQ¿UP\RXUDQVZHUE\
drawing two pulses that move closer to each other, cross and then moves away from each other.
______________________________________________________________________________
_______________________________________________________________________________
___________________________________________________________________________________
6
TOPIC 1
Activity 2
SUPERPOSITION OF PULSES
1. State the principle of superposition.
__________________________________________________________________________________________
______________________________________________________________________________________________
__________________________________________________________________________________________
2. 2.1 What is the effect (result) called that two pulses have on each other when they are superimposed?
_______________________________________________________________________________________
2.2 Define the effect named in Question 2.1.
_______________________________________________________________________________________
_______________________________________________________________________________________
3. 3.1 When does constructive interference occur between pulses?
_______________________________________________________________________________________
_______________________________________________________________________________________
3.2 Use a sketch of pulses in a rope to explain constructive interference.
3.3 When does destructive interference occur with pulses?
_______________________________________________________________________________________
_______________________________________________________________________________________
3.4 Use a sketch of pulses in a rope to explain destructive interference.
7ZRSXOVHV$DQG%PRYHUWRZDUGVHDFKRWKHUDWDVSHHGRIP.s-1 and have the position and shape at time
W VDVVKRZQLQWKHILJXUH7KHJULGOLQHVUHSUHVHQWFPE\FP
4.1 Use the equation speed = distance ÷ time and determine the time that it takes for one pulse to move each
FP
FP
t=0s
_____________________________________________
A
B
_____________________________________________
a
b
_____________________________________________
_____________________________________________
WAVES, SOUND AND LIGHT
7
4.2 Use the grid lines given and draw the position of the
pulses at the times t = 0,1 s; 0,2 s; 0,3 s and 0,4 s.
t=1s
4.3 At which time did the fronts (i.e. the parts a and b)
of the two pulses meet?
______________________________________
4.4 At what time did the two pulses completely overlap,
i.e. superimpose?
t=2s
______________________________________
:KDWGRZHFDOOWKHDOJHEUDLFVXPRIWKHDPSOLWXGHV
of the pulses at the moment mentioned in Question
4.4?
______________________________________
t=3s
4.6 The fact that the two pulses superimpose, indicates
that interference occurred. What type of interference
occurred here?
______________________________________
t=4s
7ZRSXOVHV)DQG*PRYHWRZDUGVHDFKRWKHUDWDVSHHGRIP.s-1 and have the position and shape at time
W VDVVKRZQLQWKH¿JXUH7KHJULGOLQHVDUHPPDSDUW
8VHWKHHTXDWLRQVSHHG GLVWDQFH·WLPHDQG
determine the time that it takes for one pulse to
move each 20 mm.
20 mm
t=0s
)
______________________________________
______________________________________
a
b
______________________________________
______________________________________
G
8VHWKHJULGOLQHVJLYHQDQGGUDZWKHSRVLWLRQRIWKHSXOVHVDWWKHWLPHVW VVVDQGV
t=1s
8
t=2s
TOPIC 1
t=3s
t=4s
$WZKLFKWLPHGLGWKHIURQWVLHWKHSDUWVDDQGERIWKHWZRSXOVHVPHHW"
________________________________________________________________________________________
$WZKLFKWLPHGLGWKHWZRSXOVHVRYHUODSFRPSOHWHO\LHVXSHULPSRVH"
________________________________________________________________________________________
:KDWGRZHFDOOWKHDOJHEUDLFVXPRIWKHDPSOLWXGHVRIWKHSXOVHVDWWKHWLPHPHQWLRQHGLQ4XHVWLRQ"
________________________________________________________________________________________
7KHIDFWWKDWWKHWZRSXOVHVDUHVXSHULPSRVHGLQGLFDWHVWKDWLQWHUIHUHQFHRFFXUUHG:KLFKW\SHRI
interference occurred here?
________________________________________________________________________________________
6. Pulses form part of our daily lives. It can be the result of a pile-up due to collisions on a highway, spectators
that stand and sit during a Mexican wave at a sports meeting, or the sudden compression of air during an explosion.
Two pulses P and Q in a rope move closer together at the same speed. Pulse P has an amplitude of +4,0
cm at position X. Pulse Q has an amplitude of -6,0 cm at position Z. Points X and Z are the same distance
from point Y. Both pulses have a length of 8,0 cm. Pulse P and Q meet each other at position Y. Assume that
no energy is lost.
8,0 cm
:ULWHWKHGH¿QLWLRQRIDSXOVH
P
____________________________________
+4,0 cm
Z
____________________________________
____________________________________
X
Y
6.2 Write the name of the phenomenon that occurs
when the two pulses meet at position Y.
____________________________________
6.3 Make a labelled sketch to indicate what happens
when pulses P and Q meet at position Y. Also
indicate the pulse length.
-6,0 cm
Q
8 0 cm
6.4 Make a labelled sketch to indicate what would
happen when pulse P reaches position Z.
3XOVH3PRYHVIURPSRVLWLRQ;WRSRVLWLRQ=DGLVWDQFHRIPLQV&DOFXODWHWKHVSHHGRISXOVH3
____________________________________
____________________________________
____________________________________
WAVES, SOUND AND LIGHT
9
7. The following sketches show the amplitudes of a number of pulses that approach each other and then
superimpose when they cross. Calculate and give the directions of the devoid amplitudes. (Positive (+)
indicates the upward direction.) Also specify whether it is an example of constructive or destructive superposition.
+5 cm
7.1 +5 cm
7.2
+3 cm
-3 cm
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
7.3 +10 cm
7.4
+5 cm
-8 cm
-10 cm
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
__________________________________
8. A pulse with amplitude -7 mm moves to the right and one with an amplitude of + 12 mm moves to the left.
8.1 Draw separate diagrams to show the pulses that approach each other, cross and then moves apart form
each other.
8.2 Calculate the amplitudes of the disturbance when they cross.
____________________________________________
____________________________________________
7KHIROORZLQJWDEOHVKRZVWKHDPSOLWXGHVRIDQXPEHURISXOVHVWKDWDSSURDFKHDFKRWKHUDQGWKHQ superimposes when they cross.
Calculate and give the direction of the devoid amplitudes. (Positive (+) indicates the upwards direction.)
Amplitudes
Pulse X
Pulse Y
+12 mm
PP
+10 mm
PP
-17 cm
-8 cm
FP
-26 mm
-4 m
+4 m
-7 m
10
Superposition
-2 m
TOPIC 1
10. The following unusual pulse forms near each other in a medium. Each pulse moves at 1 m.s-1. Sketch the
resultant pulse that forms after 1s, 2s, 3s and 4s.
10.1
10.2
10.3
t =0s
t =0s
t =0s
t =1s
t =1s
t =1s
t =2s
t =2s
t =2s
t =3s
t =3s
t =3s
t =4s
t =4s
t =4s
t =0s
t =0s
t =0s
t =1s
t =1s
t =1s
t =2s
t =2s
t =2s
t =3s
t =3s
t =3s
t =4s
t =4s
t =4s
WAVES, SOUND AND LIGHT
11
Chapter
2 TRANSVERSE WAVES
TRANSVERSE WAVES
A WAVE
A wave is the regular sequence of pulses. A wave is a way that energy is transmitted from one point to another
in a medium in the range of consecutive pulses (or disturbances).
There are two types of wave motions, namely transverse waves and longitudinal waves. Examples of transverse
waves are water waves, perpendicular waves in a string or spring, waves in a guitar string and electromagnetic
waves. Examples of longitudinal waves are parallel waves in a spring and sound waves.
TRANSVERSE WAVES
direction of disturbance
A transverse wave can be formed by holding
one end of a spring (or rope) and moving
the other end back and forth. A series of
transverse pulses move in the spring, with
the disturbance in the spring perpendicular
to the direction that the pulse moves in. A
transverse wave motion is created.
propagation direction
(direction of motion)
Figure 1 A transverse wave movement
A transverse wave is a wave in which the disturbance of the medium is
perpendicular to the propagation direction of the wave.
PROPERTIES OF TRANSVERSE WAVES
Consider the following graphical representation of a transverse wave:
wave length
crest
Ȝ
y
x
position of rest
or equilibrium
A
amplitude
A
z
trough
Figure 2 Graphical representation of a transverse wave.
‡7KHFHQWUHOLQHVKRZVWKHSRVLWLRQRIWKHXQGLVWXUEHGVWULQJRUURSH,WLVFDOOHGWKHposition of rest or equilibrium.
‡7KHKLJKHVWSRLQWRIWKHZDYHLVFDOOHGDcrest and the lowest point a trough.
‡7ZRSRLQWVRQDZDYHPRYHVLQSKDVHZKHQWKH\PRYHLQWKHVDPHGLUHFWLRQDWWKHVDPHVSHHGDQGKDYHWKH same displacement from the position of rest. Points x and y are in phase. Any two crests or two troughs are
always in phase.
‡7ZRSRLQWVRQDZDYHPRYHRXWRISKDVHLIWKH\PRYHLQVXFKDZD\WKDWWKH\UHDFKDSRVLWLRQDWGLIIHUHQWWLPHV
(Points x and z as well as y and z are out of phase). A crest and a trough are always out of phase.
‡7KHwavelength (Ȝ, pronounced “lambda”) is the distance between two successive points that are in
phase. The distance between two crests or two troughs is one wavelength and is measured in meter (m).
‡7KHfrequency (ƒ)LVWKHQXPEHURIZKROHZDYHVWKDWPRYHSDVWD¿[HGSRLQWLQRQHVHFRQGDQGLVPHDVXUHG
in hertz (Hz) The frequency of the waves are naturally the same as the frequency of the vibrator that generate
the waves.
‡7KHperiod (T) of the wave motion is the time that it takes to complete one wave (full wave) and is measured
in seconds (s).
‡7KHUHODWLRQEHWZHHQWKHIUHTXHQF\(ƒ) and period (T) is represented by: ƒ = 1_
T
1
_______
For a wave the distance covered in one period is one wavelength and the frequency is period .
From this we can derive that, T = 1_ , so that: (table follow)
f
12
TOPIC 1
Period (T)
decreases
increases
Frequency (f)
increases
decreases
Number wavelength per second
increases
decreases
Relation between period, frequency and wavelength.
WAVE SPEED
Direction wherein waves move
t=0
The wave speed, v, is the distance that the wave (or crest of the
wave) covers in a second and is measured in meter per second
(m.s-1 of m/s). A wave (or crest of a wave) that eg. moves a distance
of 30 m in 3 s thus has a speed of 30/3 = 10 m.s-1.
Figure 3 shows that the time that it takes to make one complete wave,
LVRQHSHULRG,QRQHSHULRG(T) the wave moves (or crest of the wave)
a distance of one wave length (Ȝ) and the frequency (ƒ) is equal to
1/period. Therefore, the wave speed:
distance covered
wavelength (Ȝ)
v = ______________ = ___________
time
period (T)
1
t = _T
4
1
t = _T
2
3
t = _T
4
1
_
, is v = ƒȜ
T
t=T
Wave speed (v measured in m.s-1) is thus the product of the
frequency (ƒ measured in Hz) and wave length (Ȝ measured in m)
Ȝ
of the wave.
Figure 3 After one period a wave moves the
_
distance of one wavelength.
Wave speed can thus be calculated with: v = ƒȜor v = Ȝ
T
Because ƒ =
Example
1
1. A transverse wave is generated in a rope by shaking one end of the rope as shown in Figure 4. The hand
moves up and down with a frequency of 5 Hz.
6 cm
4 cm
)RUWKLVZDYHPRWLRQ¿QG
1.1 the frequency
1.3 the period
1.5 the amplitude
1.2 the wavelength
1.4 the speed
Solution
1.1 Frequency (ƒ) of the wave = frequency of the hand = 5 Hz
1.2 Wavelength (Ȝ) of the wave = distance between troughs = 4 cm = 0,04 m
1=_
1 = 0,2 s
1.3 Period (T) of the wave = _
ƒ 5
1.4 Speed of the wave: v = ƒȜ = (5)(0,04) = 0,2 m.s-1
1.5 Amplitude (A) of the wave = displacement of a crest (or trough) = 3 cm
2. If the rate at which the rope is shaken above, is doubled, while all the other factors stay the same, which
changes (if any) will take place for the following for this wave motion?
2.1 The frequency
2.2 The wavelength
2.3 The period
2.4 The wave speed
2.5 The amplitude
Solution
2.1 The frequency doubles.
2.2 Because v = ƒȜ and v are constant, the wavelength is halved.
2.3 Because f = 1_, the period is halved.
T
2.4 The wave speed stays unchanged.
2.5 The amplitude of the wave stays unchanged.
WAVES, SOUND AND LIGHT
13
Example
2
A cork stopper on the surface of a pool moves up and down every second. The ripples have a wavelength of
20 cm. If the cork stopper is 2 m from the edge of the pool, how long will it take for a ripple that moves past the
cork stopper to reach the edge of the swimming pool?
Solution
The time that it takes for the ripples to reach
D
_
_
D
the edge of the swimming pool, is obtained from: t = v (of v = t )
We also know that: v = ƒȜ
__
D
So that: t = ƒȜ
2
m
= ___________
(1 Hz)(0,2 m)
2m
= ___________
(1 s-1)(0,2 m)
= 10 s
A ripple that moves past the cork, will take 10 s to reach the edge of the swimming pool.
Practical Activity
1
Generating transverse waves
WHAT YOU NEED
‡ spring or sturdy rope
Method:
+ROGWKHVSULQJRQWKHZRUNEHQFKRUÀRRUDVVKRZQLQ)LJXUHEHORZ
2. Let a friend hold one end of the spring tightly (or attach it to an object that cannot move).
3. Pull the free end of the spring and move it to and fro in a regular repetitive motion.
Figure 5 Demonstration of a transverse
wave using a spring.
Figure 6 Transverse wave pattern in a spring.
Questions
1. Why can we say that the wave pattern in the spring (or rope) is that of a “transverse wave”?
________________________________________________________________________________________
_______________________________________________________________________________________
2. Make a sketch of your observations. Indicate the following on your sketch:
Equilibrium ; amplitude ; wavelength ; crest ; trough ; propagation direction
3. 3.1 On your sketch above, mark a point x and a point y to indicate two points in phase on the wave.
3.2 On your sketch above, mark a point m and a point n to indicate two points out of phase on the wave.
14
TOPIC 1
Activity 1
TRANSVERSE WAVES
1. Look at the sketch of your observation in the Practical Activity above, and describe in words the meaning of the
following terms for a transverse wave.
1.1 A crest:_______________________________________________________________________________
1.2 A trough:______________________________________________________________________________
________________________________________________________________________________________
1.3 Wavelength:___________________________________________________________________________
________________________________________________________________________________________
1.4 Frequency:____________________________________________________________________________
________________________________________________________________________________________
1.5 Amplitude :_____________________________________________________________________________
________________________________________________________________________________________
1.6 Points in phase :_________________________________________________________________________
________________________________________________________________________________________
1.7 Points out of phase: _____________________________________________________________________
________________________________________________________________________________________
2. The diagram below shows different points on a transverse wave.
D
A
F
B
E
C
2.1 Distinguish between a “pulse” and a “wave”.
________________________________________________________________________________________
________________________________________________________________________________________
___________________________________________________________________________________________
_________________________________________________________________________________
_____________________________________________________________________________________
2.2 Use only the symbols on the diagram to indicate the following:
2.2.1 an amplitude: _____________________
2.2.2 a crest: ______________________________
2.2.3 a trough: _____________________
2.2.4 one wavelength: ______________________
2.2.5 any two points in phase
2.2.6 any two points out of phase
________________________________
____________________________________
3. When the particles of a medium moves perpendicular to the direction of propagation of the wave, the wave is
known as a _____________________ wave.
WAVES, SOUND AND LIGHT
15
4. A transverse wave moves downwards. In which direction do the particles move in the medium.
__________________________________________________________________________________________
5. Study the diagram below and answer the questions that follow:
B
A
CD
5.1 The wavelength of the wave is indicated with the letter ________ .
5.2 The amplitude of the wave is indicated by the letter ________ .
6. Draw 2 wavelengths of the following transverse wave.
Wave 1 : Amplitude = 1 cm and wavelength = 6 cm
Wave 2 : Distance from crest to trough (vertical) = 3 cm, crest to crest distance (horizontal) = 8 cm
1 cm
1 cm
7. You are given the following transverse wave.
1
0
12
4
3
-1
Draw the following:
7.1 A wave with twice the amplitude
of the above wave.
7.2 A wave with half the amplitude of the
above wave.
1
0
-1
16
1
1
2
3
4
0
1
2
3
4
-1
TOPIC 1
7.3 A wave that moves at the same speed, but
with twice the frequency of the given wave.
7.4 A wave that moves at the same speed,but
half the frequency of the given wave.
1
0
1
1
2
0
4
3
-1
3
4
7.6 A wave with half the wavelength of the
given wave.
1
1
1
2
0
4
3
-1
1
2
3
4
-1
7.7 A wave that moves at the same speed, but with
a period that is double the size of the
given wave.
7.8 A wave that moves at the same speed, but
half of the period of the given wave.
1
0
2
-1
7.5 A wave with twice the wavelength of the given
wave.
0
1
1
1
2
0
4
3
-1
1
2
3
4
-1
8. Study the following diagram and answer the questions:
Direction of motion
C
B
K
D
J
E
,
A
F
H
G
WAVES, SOUND AND LIGHT
L
M
Q
N
P
O
17
8.1 Identify two sets of points that are in phase: ___________________________________________________
8.2 Identify two sets of points that are out of phase: _______________________________________________
8.3 Identify two points that indicate a wave length: ________________________________________________
8.4 What type of wave movement is represented by the diagram? Give a reason for your answer.
______________________________________________________________________________________
______________________________________________________________________________________________
8.5 As the period of this wave increases, will the frequency increase / decrease / not change.
Give a reason for your answer.
______________________________________________________________________________________
_____________________________________________________________________________________________
______________________________________________________________________________________________
9. Give the meaning of each of the following symbols as well as the unit in which each is measured with respect to
waves.
T : _______________________________________________________________________________________
ƒ : _______________________________________________________________________________________
Ȝ : _______________________________________________________________________________________
v : _______________________________________________________________________________________
10. Use the symbols above and write a formula to calculate the speed of a wave:
10.1 in terms of ƒ and Ȝ
10.2 in terms of T and Ȝ
__________________
11. 11.1 Calculate the speed of a wave with a
wavelength of 10 m, that is supplied by a
vibrating source with a frequency of 0,25 Hz.
___________________________________
11.2 Waves with a frequency of 1,5 Hz are
generated in a spring. The wavelength of
the waves is 0,3 m. Calculate the speed of
the waves.
___________________________________
___________________________________
___________________________________
________________________________
________________________________
11.3 A wave that moves at the speed of 100
m.s-1, has a wavelength of 40 m.
Calculate the frequency.
11.4 A wave that moves at the speed of 300 m.s-1
has a wave length of 1 500 m.
Calculate the frequency of the wave.
___________________________________
___________________________________
___________________________________
___________________________________
________________________________
________________________________
________________________________
18
___________________
________________________________
TOPIC 1
11. 11.5 Calculate the wavelength of a wave with
a speed of 10 m.s-1 and a frequency of 20 Hz.
11.6 Calculate the wavelength of a wave with
a speed of 80 m.s-1 and the frequency of 50 Hz.
___________________________________
___________________________________
___________________________________
___________________________________
________________________________
________________________________
________________________________
________________________________
7KHGLDJUDPVKRZVNLGVWKDWXVHDELJSODQNDVDÀRDWLQWKHVZLPPLQJSRRORIDELJVSRUWVFHQWUH. A wave
machine in the swimming pool causes 24 waves per minute to be created on the surface of the water.
12.1 Show that the frequency of the wave
machine is 0,4 Hz.
__________________________________
__________________________________
_______________________________
12.2 The wavelength of the waves in the pool
is 4 m. Calculate the speed of the waves
in the swimming pool.
0,5 m
12.3 The board moves up and down on the
waves so that it reaches a vertical height of
0,5 m. What is the amplitude of the waves?
__________________________________
__________________________________
__________________________________
__________________________________
_______________________________
13. A transverse wave moves at a constant speed with an amplitude of 10 cm and a frequency of 30 Hz.
The horizontal distance of a crest to the nearest trough is measured as 5 cm. Determine the
13.1 period of the wave.
13.2 speed of the wave.
__________________________
____________________________
__________________________
____________________________
__________________________
____________________________
14. John stands on the harbour wall and sees four wave crests pass in 8 s. He estimates the distance between the
WZRVXFFHVVLYHFUHVWVDVP7KHWLPHLVPHDVXUHGIURPWKHEHJLQQLQJRIWKH¿UVWFUHVWWRWKHHQGRIWKH
fourth crest.
14.1 Calculate the period of the wave.
14.2 Calculate the speed of the wave.
__________________________
____________________________
__________________________
____________________________
__________________________
____________________________
15. A wave moves along a rope at a speed of 15 m.s-1. If the frequency of the source of the wave is 7,5 Hz , calculate
15.1 wavelength of the wave.
15.2 the period of the wave.
__________________________
____________________________
__________________________
____________________________
WAVES, SOUND AND LIGHT
19