Compiled by: A. Olivier

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2 Other books in this series Warning!! All rights reserved according to the South African copyright act. No part of this book may be reproduced by photocopying or any other method without written permission of the publisher and writer. Any person who exercises any unauthorized act in relation to this publication may be subject to criminal prosecution and civil claims against damage. Compiled by: A. Olivier Published by: Tel: / Fax: Grade 2 Physical Sciences Theory and Workbook Book 2 (Chemistry) consists of two parts. Part 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.

3 CONTENTS Chapter Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter Chapter 2 Chapter 3 Topic WAVES, SOUND AND LIGHT TRANSVERSE PULSES Transverse Pulses In A String Or Spring Superposition Of Pulses Transverse Waves Topic 2 ELECTRICITY AND MAGNETISM MAGNETISM Magnetic Fields, Magnetic Poles And Forces Static Electricity TRANSVERSE WAVES LONGITUDINAL WAVES Longitudinal Waves In A Rope Or Spring Sound Waves SOUND ELECTROMAGNETIC RADIATION The Nature Of Electromagnetic Radiation ELECTROSTATICS ELECTRIC CIRCUITS Circuits Potential Difference And Emf Current Resistance Resistors In Series And Parallel

4 Chapter Chapter 2 Chapter 3 Chapter 4 Topic 3 MECHANICS VECTORS AND SCALARS Introduction To Vectors And Scalars MOTION IN ONE DIMENSION Position, Displacement And Distance Speed And Velocity Acceleration 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 ENERGY Gravitational Potential Energy And Kinetic Energy Conservation Of Mechanical Energy

5 Chapter TRANSVERSE PULSES TRANSVERSE PULSES IN A STRING OR SPRING PULSES 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 2 below shows a single pulse that moves along a rope (as medium). Movement of pulse Figure A slinky (spiral), helix spring (weak spring) or a heavy rope can be used to study waves. Helix spring Heavy rope Slinky Figure 2 A pulse moves along 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 pulse. It causes a disturbance that moves along the rope. A pulse is a single disturbance in a medium (spring or rope) that moves from one point to another. The pulse is created by the source (hand) and moves down the rope, but the rope does not move with. The particles 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). displacement y x distance pulse length amplitude Figure 4 Pulse terminology pulse speed disturbance or displacement y) position of rest equilibrium 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

6 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: D v = _ 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 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 - D v = _ t = 4 m = 0,8 m.s - Practical Activity Generation of transverse pulses WHAT YOU NEED spiral spring or strong rope small piece of string or ribbon To view the PHET pulse in a rope simulation, visit: phet.colorado.edu/sims Choose waves and then waves on string. Method: 2. Have a friend hold the other end of the spring tightly (or attach it to an object that will not move) Mark point (A) with a small piece of string on the spring. 3. Pull the free end of the spring and quickly move it to one side and back to its original position to generate a pulse. (A pulse is only one movement of the spring). A Figure 5 Demonstration of a transverse pulse with the aid of a spiral spring. Questions. 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? 2 TOPIC

7 Exersise TRANSVERSE PULSES IN A ROPE OR SPRING 2. Liza uses a spiral spring to generate a transverse pulse. 2. 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..s -. How WAVES, SOUND AND LIGHT 3

8 .s -. How 3.4 How long will it take for a pulse that moves.s - 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 3 m 4. 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). A coin on the furthermost end of the rug is brought into motion after 2 s. 4.4 Calculate the speed of the pulse. B A 4 TOPIC

9 SUPERPOSITION OF PULSES SUPERPOSITION when they pass each other. Figure 8, 9 and 0 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 0 After the two pulses cross each other, they move further unchanged. Careful observation shows that: bigger as that of any of the other original pulses. 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 of interference are distinguished, i i d namely constructive interference and destructive interference. 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 a b b a b a Figure 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. a b a + b b a Figure 2 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 () (2) 40 mm 40 mm 50 mm WAVES, SOUND AND LIGHT 5

10 Solution Practical Activity 2 Observe constructive and destructive interference WHAT YOU NEED wave tank water 2 rulers Method: 0 mm. placing a ruler in the water. placing two rulers simultaneously in the water and observe what happens when the pulses cross and after they have Figure 3 A Wave tank crossed. times. And observe what happens when the pulses cross and after they have crossed. Questions. The following diagram shows how the pulses that are formed simultaneously in the water moves towards 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 drawing two pulses that move closer to each other, cross and then moves away from each other. 6 TOPIC

11 Activity 2 SUPERPOSITION OF PULSES. State the principle of superposition 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 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..s - and have the position and shape at time 4. Use the equation speed = distance time and determine the time that it takes for one pulse to move each t = 0 s A B a b WAVES, SOUND AND LIGHT 7

12 4.2 Use the grid lines given and draw the position of the pulses at the times t = 0, s; 0,2 s; 0,3 s and 0,4 s. t = s 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 = 2 s of the pulses at the moment mentioned in Question 4.4? t = 3 s 4.6 The fact that the two pulses superimpose, indicates that interference occurred. What type of interference occurred here? t = 4 s.s - and have the position and shape at time 20 mm determine the time that it takes for one pulse to move each 20 mm. t = 0 s a b G t = s t = 2 s 8 TOPIC

13 t = 3 s t = 4 s 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 P +4,0 cm Z 6.2 Write the name of the phenomenon that occurs when the two pulses meet at position Y. X Y -6,0 cm Q 80 cm 6.3 Make a labelled sketch to indicate what happens 6.4 Make a labelled sketch to indicate what would when pulses P and Q meet at position Y. Also happen when pulse P reaches position Z. indicate the pulse length. WAVES, SOUND AND LIGHT 9

14 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 cm +3 cm cm cm cm -0 cm -8 cm 8. A pulse with amplitude -7 mm moves to the right and one with an amplitude of + 2 mm moves to the left. 8. 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. superimposes when they cross. Calculate and give the direction of the devoid amplitudes. (Positive (+) indicates the upwards direction.) Amplitudes Pulse X Pulse Y Superposition +2 mm +0 mm -7 cm -8 cm -26 mm -4 m +4 m -7 m -2 m 0 TOPIC

15 0. The following unusual pulse forms near each other in a medium. Each pulse moves at m. s -. Sketch the resultant pulse that forms after s, 2s, 3s and 4s t = 0 s t = 0 s t = 0 s t = s t = s t = s t = 2 s t = 2 s t = 2 s t = 3 s t = 3 s t = 3 s t = 4 s t = 4 s t = 4 s t = 0 s t = 0 s t = 0 s t = s t = s t = s t = 2 s t = 2 s t = 2 s t = 3 s t = 3 s t = 3 s t = 4 s t = 4 s t = 4 s WAVES, SOUND AND LIGHT

16 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 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. direction of disturbance propagation direction (direction of motion) Figure 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 A x y position of rest or equilibrium A amplitude z trough Figure 2 Graphical representation of a transverse wave. position of rest or equilibrium. crest and the lowest point a trough. same displacement from the position of rest. Points x and y are in phase. Any two crests or two troughs are always in phase. (Points x and z as well as y and z are out of phase). A crest and a trough are always out of phase. wavelength (, 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). frequency (ƒ) in hertz (Hz) The frequency of the waves are naturally the same as the frequency of the vibrator that generate the waves. period (T) of the wave motion is the time that it takes to complete one wave (full wave) and is measured in seconds (s). (ƒ) and period (T) is represented by: ƒ = _ T For a wave the distance covered in one period is one wavelength and the frequency is period. From this we can derive that, T = _, so that: (table follow) f 2 TOPIC

17 WAVE SPEED 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 - 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 = 0 m.s -. Figure 3 shows that the time that it takes to make one complete wave, (T) the wave moves (or crest of the wave) a distance of one wave length () and the frequency (ƒ) is equal to /period. Therefore, the wave speed: distance covered wavelength () v = = time period (T) Because ƒ = _ T, is v = ƒ Wave speed (v measured in m.s - ) is thus the product of the frequency (ƒ measured in Hz) and wave length ( measured in m) of the wave. Wave speed can thus be calculated with: Period (T) Frequency (f) Number wavelength per second decreases increases increases increases decreases decreases Relation between period, frequency and wavelength. v = ƒor v = _ T Direction wherein waves move t = 0 t = _ T 4 t = _ T 2 3 t = _ T 4 t = T Figure 3 After one period a wave moves the distance of one wavelength. Example. 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. 4 cm 6 cm. the frequency.2 the wavelength.3 the period.4 the speed.5 the amplitude Solution. Frequency (ƒ) of the wave = frequency of the hand = 5 Hz.2 Wavelength () of the wave = distance between troughs = 4 cm = 0,04 m.3 Period (T) of the wave = _ = _ = 0,2 s ƒ 5.4 Speed of the wave: v = ƒ = (5)(0,04) = 0,2 m.s -.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. The frequency 2.2 The wavelength 2.3 The period 2.4 The wave speed 2.5 The amplitude Solution 2. The frequency doubles. 2.2 Because v = ƒ and v are constant, the wavelength is halved. 2.3 Because f = _, 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 3

18 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 the edge of the swimming pool, is obtained from: t = D D v _ (of v = _ t ) We also know that: v = ƒ D So that: t = ƒ 2 m = ( Hz)(0,2 m) 2 m = ( s - )(0,2 m) = 0 s A ripple that moves past the cork, will take 0 s to reach the edge of the swimming pool. Practical Activity WHAT YOU NEED spring or sturdy rope Generating transverse waves Method: 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. 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 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. 4 TOPIC

19 Activity TRANSVERSE WAVES. 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.. A crest:.2 A trough:.3 Wavelength:.4 Frequency:.5 Amplitude :.6 Points in phase :.7 Points out of phase: 2. The diagram below shows different points on a transverse wave. A D B E F 2. Distinguish between a pulse and a wave. C 2.2 Use only the symbols on the diagram to indicate the following: 2.2. an amplitude: a crest: a trough: one wavelength: any two points in phase 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 5

20 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: A B 5. The wavelength of the wave is indicated with the letter. 5.2 The amplitude of the wave is indicated by the letter. CD 6. Draw 2 wavelengths of the following transverse wave. Wave : Amplitude = cm and wavelength = 6 cm Wave 2 : Distance from crest to trough (vertical) = 3 cm, crest to crest distance (horizontal) = 8 cm cm cm 7. You are given the following transverse wave Draw the following: 7. A wave with twice the amplitude 7.2 A wave with half the amplitude of the of the above wave. above wave TOPIC

21 7.3 A wave that moves at the same speed, but 7.4 A wave that moves at the same speed,but with twice the frequency of the given wave. half the frequency of the given wave A wave with twice the wavelength of the given 7.6 A wave with half the wavelength of the wave. given wave A wave that moves at the same speed, but with 7.8 A wave that moves at the same speed, but a period that is double the size of the half of the period of the given wave. given wave Study the following diagram and answer the questions: Direction of motion C K B D J L A E M Q F H N P G O WAVES, SOUND AND LIGHT 7

22 8. 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 : : v : 0. Use the symbols above and write a formula to calculate the speed of a wave: 0. in terms of ƒ and 0.2 in terms of T and.. Calculate the speed of a wave with a wavelength of 0 m, that is supplied by a vibrating source with a frequency of 0,25 Hz..3 A wave that moves at the speed of 00 m.s -, has a wavelength of 40 m. Calculate the frequency..2 Waves with a frequency of,5 Hz are generated in a spring. The wavelength of the waves is 0,3 m. Calculate the speed of the waves..4 A wave that moves at the speed of 300 m.s - has a wave length of 500 m. Calculate the frequency of the wave. 8 TOPIC

23 ..5 Calculate the wavelength of a wave with a speed of 0 m.s - and a frequency of 20 Hz..6 Calculate the wavelength of a wave with a speed of 80 m.s - and the frequency of 50 Hz.. A wave machine in the swimming pool causes 24 waves per minute to be created on the surface of the water. 2. Show that the frequency of the wave machine is 0,4 Hz. 2.2 The wavelength of the waves in the pool is 4 m. Calculate the speed of the waves in the swimming pool. 0,5 m 2.3 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? 3. A transverse wave moves at a constant speed with an amplitude of 0 cm and a frequency of 30 Hz. The horizontal distance of a crest to the nearest trough is measured as 5 cm. Determine the 3. period of the wave. 3.2 speed of the wave. 4. John stands on the harbour wall and sees four wave crests pass in 8 s. He estimates the distance between the fourth crest. 4. Calculate the period of the wave. 4.2 Calculate the speed of the wave. 5. A wave moves along a rope at a speed of 5 m.s -. If the frequency of the source of the wave is 7,5 Hz, calculate 5. wavelength of the wave. 5.2 the period of the wave. WAVES, SOUND AND LIGHT 9