Presentation on theme: "Module 4.1 – Introduction to Waves"— Presentation transcript:
1 Module 4.1 – Introduction to Waves Waves are caused by vibrations, such as objects undergoing simple harmonic motion. Although water waves, sound waves, springs, and light all seem very different, they share many properties that can be explained using a wave model. This module introduces trainees to some general wave properties which will later be applied to specific types of waves.
2 Period and Frequency Period – time it takes for one complete cycle Frequency – number of cycles per unit time
3 ExampleA child swings back and forth on a swing 15 times in 30.0 s. Determine the frequency and period of the swing.
4 Wave TerminologyWave – a disturbance that transfers energy
7 1D Wave Properties Wave Simulator Wave speed depends only on the mediumUpright reflected waveHeavy mediumLight MediumInverted reflected waveLight mediumHeavy Medium
8 SuperpositionWhen waves collide they simply pass through one another unchanged. They continue on as if there were no interaction.While the waves overlap, they temporarily produce a resultant wave due to interference. The displacement of the medium is the sum of the displacements of each component waveConstructive InterferenceDestructive Interference
10 Resonance and Standing Waves Resonance – achieved when energy is added to a system at the same frequency as its natural frequency;Results in maximum amplitude.Standing Wave – example of resonance
11 Check Your LearningThe ? of a wave depends only on the medium in which it is travelling.FrequencyPeriodSpeedWavelength(c) speedWhen a wave passes from one medium to another, the ? must stay the same.Amplitude(b) frequency
12 Check Your LearningA wave in which the medium moves parallel to the medium is called a ? wave.ElectromagneticLongitudinalMechanicalTransverse(b) longitudinalThe vertical distance from the top of a crest to the bottom of a trough is 34.0 cm. The amplitude of this wave is8.5 cm17.0 cm34.0 cm68.0 cm(b) 17.0 cm
13 Check Your LearningA pulse goes into a medium that is less dense. The reflected pulse isFasterInvertedLargerUpright(d) uprightResonance occurs when one object causes a second object to vibrate. The second object must have the same naturalAmplitudeFrequencySpeedWavelength(b) frequency
14 Check Your LearningA wave source has a period of 0.20 s. What is the frequency?0.20 Hz1.0 Hz5.0 Hz20. Hz(c) 5.0 Hz
15 Wave EquationWave velocity – the velocity at which the wave crests (or any other part of the wave) move;not the same as the velocity of a particle of the medium.
16 Example 1A hiker shouts toward a vertical cliff 685 m away. The echo is heard 4.00 s later. The wavelength of the sound is m.What is the speed of sound in air?What is the frequency?What is the period of the wave?
18 Example 2Water waves have a wavelength of 3.2 m and a frequency of 0.78 Hz.At what rate does a stationary boat bob up and down?If the boat starts moving into the waves (in the opposite direction to) at a speed of 5.0 m/s, at what rate will the boat bob up and down now?
19 SolutionSince the boat is not moving, it will bob up and down at the same frequency as the waves.
20 Check Your LearningWater waves in a lake travel 4.4 m in 1.8 s. The period of oscillation is 1.2 s. What is the speed and wavelength of the water waves?
27 Check Your Learning The direction a wave moves is Parallel to the wavefronts.Perpendicular to the wavefronts.In the direction of increasing density.In the direction of increasing wavelength.(b) Perpendicular to the wavefronts.The process by which a wave bounces off an obstacle in its path is calledDiffractionReflectionRefractionSuperposition(b) Reflection
28 Check Your LearningThe bending of waves as they go through a small opening is calledDiffractionReflectionRefractionSuperposition(a) DiffractionThe bending of waves as they go from one medium to a new medium is called(c) Refraction
29 Check Your LearningWhen two waves interfere with one another, the word interfere meansOne wave prevents the other wave from finishing its cycle.One wave stops moving while the other passes.The motion we observe is the sum of the motions of the two individual waves.The wave with the larger amplitude grows and the wave with the smaller amplitude shrinks.(c) The motion we observe is the sum of the motions of the two individual waves.
30 Module Summary In this module you have learned that Mechanical waves need a medium while electromagnetic ones do not.Mechanical waves can be transverse or longitudinal.The correct terminology to use when describing waves, such as: period, frequency, crest, trough, amplitude, wavelengthThe speed of a wave depends only upon the medium in which it is travelling.Waves will be both reflected and transmitted at a boundary.
31 Module SummaryThe frequency of a wave does not change when going from one medium to another one.When waves interfere with one another, they can interfere constructively or destructively before passing through one another unchanged.A standing wave is an example of resonance in a medium.All waves are governed by the wave equation
32 Module SummaryAll two-dimensional waves obey the law of reflection, which states that the angle of incidence is equal to the angle of reflectionAll two-dimensional waves undergo refraction, diffraction, and interference.
33 Module 4.2 – Sound WavesIn this module, the wave properties studied in module 7.2 will be looked at in greater depth as they apply to sound waves. Although these properties can be observed in general with all waves, they are often easily observable and can be demonstrated using these specific types of waves. Sound waves are used in a variety of techniques in exploring for oil and minerals.
34 Sound Waves Mechanical Wave (longitudinal) Series of compressions and rarefactions
36 Range of Hearing Human Hearing infrasonic 20 Hz 20000 Hz ultrasonic Range decreases as we ageMany animals can hear above our range of hearing
37 Speed of Sound Mechanical waves need a medium Medium determines speed of soundMaterialSpeed of Sound (m/s)Air (at 0oC and 101 kPa)331Helium (at 0oC and 101 kPa)965Fresh water (at 20oC)1482Copper5010Steel5960
38 Speed of Sound in Air Mach Number Supersonic – Mach Number is greater than one
39 ExampleA plane is flying at a speed of 855 m/s. If the air temperature is 12oC,What is the speed of sound?What is the Mach number for the plane?
43 Check Your Learning Which of the following is NOT a property of sound? AmplitudeFrequencyMassWavelength(c) MassThe average human ear cannot hear frequencies above20 Hz2000 Hz20000 Hz200000Hz(c) Hz
44 Check Your LearningWhen we describe something as supersonic we mean it isFaster than the speed of soundHigher in frequency than HzLower in frequency than 20 HzSlower than the speed of sound(a) Faster than the speed of soundWhen the amplitude of a sound wave increases,The wavelength of the sound decreasesThe sound gets louderThe pitch increasesThe speed of sound increases(b) The sound gets louder
45 Check Your Learning Sound is a longitudinal wave because The oscillations in pressure are in the same direction as the wave moves.The oscillations in pressure are perpendicular to the direction that the wave moves.The wavelength is long compared to light waves.The wavelength is always longer than the amplitude.(a) The oscillations in pressure are in the same direction as the wave moves. The wavelength of a sound wave can be calculated byMultiplying the amplitude by the frequencyDividing the amplitude by the frequencyMultiplying the speed by the frequencyDividing the speed by the frequency(d) Dividing the speed by the frequency (the wave equation)
46 Check Your Learning The speed of sound in air at 7.0oC is 331 m/s (c) 335 m/s (using v= T)A person is behind an ambulance as it moves away from her. The pitch of the sound that she hears isLower than if the ambulance was stationary.The same as if the ambulance was stationary.Higher than if the ambulance was stationary.(a) Lower than if the ambulance was stationary, since the wavelength will be larger behind the ambulance.
47 Closed Air ColumnsStanding wave in a closed air column requires a node at the closed end and an antinode at the open end of the air columnFull Standing Wave
65 Beat FrequencyBeat frequency is the absolute value of the difference between the two sources:
66 ExampleA Hz tuning fork is sounded at the same time as a key on a piano. You count 23 beats over 8.0 s. What are the possible frequencies of the piano key?
67 Check Your LearningA guitar string produces a beat frequency of 4 Hz when sounded with a 350 Hz tuning fork and a beat frequency of 9 Hz when sounded with a 355 Hz tuning fork. What is the frequency of the string?Using the first beat frequency, the possible frequencies of the string are 346 Hz or 354 Hz. Using the second beat frequency, the possible frequencies of the string are 346 Hz or 364 Hz. Since the only frequency in common is 346 Hz, this must be the frequency of the string.
68 Module Summary In this module you learned that Sound waves are longitudinal mechanical waves.Sounds can be distinguished by loudness, pitch, and quality.Sound travels through air with a speed given byThe mach number of an object can be calculated using
69 Module SummaryThe Doppler Effect and sonic booms can be explained using wave theory.Air columns resonate at their natural frequencies.Closed air columns resonate at their fundamental frequency whenOpen air columns resonate at their fundamental frequency when
70 Module Summary All of the harmonics are present in open air columns. Only the odd harmonics are present in closed air columns.When two frequencies are close but not the exact same, beats will be heard with a frequency of
71 Module 4.3 – Electromagnetic Waves The wave model of light will be applied to electromagnetic waves to further study wave properties such as reflection, refraction, and diffraction. A brief introduction to geometric optics is also included. An understanding of light is important as it applies to one of the principle means through which we obtain information, using both instruments and our sense of sight.
72 Light as a Wave Two basic methods of transferring energy: Particles – for example, a baseball travelling through the air has kinetic energy which can be transferred to another object in a collision.Waves – water waves transfer energy to the shore and cause erosion.Newton proposed a particle modelChristian Huygens proposed a wave modelNewton’s model initially accepted
73 Light as a WaveHuygens model began to gain more acceptance for the following reasons.double slit experiment to show that light passing through two slits demonstrated the same interference pattern as two sources of water waves;speed of light was shown to be lower in water than in air; this supported Huygen's theory of refraction and contradicted Newton's theory of refraction.Huygens wave model replaced by Electromagnetic Wave Model
74 Electromagnetic Spectrum Current model of light incorporates both waves and particles
77 Speed of LightSpeed accurately determined around 1900 by Michelson
78 ExampleUsing the accepted value for the speed of light, calculate the minimum frequency that would have been needed for light to be reflected into the eye of the observer in Michelson’s apparatus.
79 Check Your LearningWhy is it better when the pages of a book are rough rather than smooth and glossy?Rough pages allow light to undergo diffuse reflection, meaning the light is not all reflected in the same direction. This reduces glare from the page.A particular nearsighted person can only see clearly 0.50 m from their face. How far from a plane mirror should they be to see their image clearly?They should be 0.25 m (or less) from the mirror. Because their image is the same distance behind the mirror as they are in front of it, the total distance from the person to their image will be 0.50 m.
80 Check Your LearningWhat is the angle of incidence if the angle between a reflected ray and the mirror is 34o?If the angle between the reflected ray and the mirror is 34o, the angle of reflection (the angle with the normal) is 56o (90-34). The angle of incidence must therefore be 56o.The moon is 3.85×108 m away from the earth. How long does it take light reflected from the moon to reach the earth?
81 Coin in a Cup Demo Can See Coin Cannot See Coin Can See Coin because of refraction
82 Index of Refraction Index of refraction (n) defined as Substance Vacuum1.00AirWater1.33Ethyl alcohol1.36Quartz1.46Plexiglass1.51Crown Glass1.52Flint Glass1.65Diamond2.42
83 Example 1Calculate the speed of light in water.
85 Example 2A ray of light (travelling in air) has an angle of incidence of 30.0o on a block of quartz and an angle of refraction of 20.0o. What is the index of refraction for this block of quartz?
86 Check Your LearningThe speed of light in a clear plastic is 1.90×108 m/s. A ray of light travelling through air enters the plastic with an angle of incidence of 22°. At what angle is the ray refracted?
87 Total Internal Reflection Total internal reflection can only occur going from a high index of refraction to a lower index of refractionCritical Angle
89 Total Internal Reflection Two conditions required for total internal reflection to occur:The light must be travelling from a higher index of refraction to a lower index of refraction.The angle of incidence must be greater than the critical angle, θc, associated with the two materials.
90 Example 3What is the critical angle for the interface between air and water?
97 Example 1Red light with a wavelength of 685 nm is shone through two small slits. An interference pattern is observed on a screen that is 4.2 m away. The distance between the central maximum and the second order bright spot is 3.2 cm. What was the distance between the two slits?
100 Example 2Calculate the angle between the central maximum and the first order bright spot for a diffraction grating that has 3800 lines per centimetre on it if monochromatic light with a wavelength of 420 nm is shone on it.
101 Check Your LearningLight with a wavelength of 542 nm is shone through a diffraction grating. The third order bright spot is observed to be 74.0 cm away from the central maximum on a screen 8.20 m away. How many lines per cm does the grating have?
104 Ray DiagramsConsider an object in front of a concave mirror.
105 Rule 1Any ray drawn parallel to the principal axis will reflect through the focal point.
106 Rule 2Because of the law of reflection, the opposite must also be true. Any ray drawn through the focal point must reflect parallel to the principal axis.
107 Rule 3Any ray that goes through the center of curvature hits the mirror at a 90o angle, and so reflects back on itself.Image is real, inverted, larger
108 Check Your LearningLocate and describe the images of the object in each of the following diagrams:The image is inverted, real, and smaller.
109 Check Your LearningNotice that in this case, the reflected rays are spreading apart and will not cross. It is necessary to extend the rays behind the mirror until they cross. This image is larger, upright, and virtual.
110 Check Your LearningImage is inverted, real, and the same size.
112 Mirror EquationImage height hi is positive if upright, negative if inverted (relative to the object)The image distance di and the object distance do positive if on the reflecting side of the mirror (real) and negative if behind the mirror (virtual)The focal length f is positive if on the reflecting side of the mirror, which will always be true for concave mirrors.
113 Example 1A concave mirror has a radius of curvature of 12.0 cm. A 1.2 cm tall object is placed a distance of 8.2 cm away from the mirror.Locate the image.Calculate the height of the image.Describe the image.
115 SolutionThe image is inverted (because hi is negative), larger (because hi is bigger) and real (because di is positive).
116 Convex MirrorsRays of light diverge as if coming from the focal point
117 Convex MirrorsRules for drawing rays diagrams that we learned before are very similar for convex mirrors;instead of our incoming rays going through the focal point or the centre of curvature, they simply go toward them (since they are on the other side of the mirror).Image is always upright, smaller, virtual
118 Example 2A convex mirror has a radius of curvature of 12.0 cm. A 1.2 cm tall object is placed a distance of 8.2 cm away from the mirror.Locate the image.Calculate the height of the image.Describe the image.
119 SolutionRemember, since the mirror is convex, the radius of curvature and the focal length must be negative.
120 SolutionThe image is upright (because hi is positive), smaller (because hi is smaller) and virtual (because di is negative).
121 Check Your LearningA 5.3 cm tall object is placed 6.4 cm away from a spherical mirror. A virtual image is formed 4.2 cm from the mirror.What is the focal length of the mirror?Since the image is virtual, di must be negative
122 Check Your Learning What kind of mirror is it? Because the focal length was calculated to be negative, the mirror is convex.What is the height of the image?
123 Convex (Converging) Lens Lens is thicker in the middle
124 Concave (Diverging) Lens Lens is thinner in the middle
125 Ray Diagrams – Rule 1A ray drawn parallel to the axis is refracted by the lens so that it passes along a line through the focal point.
126 Rule 2A ray drawn on a line passing through the other focal point F’ emerges from the lens parallel to the axis.
127 Rule 3A ray directed to the center of the lens continues in a straight line.image is real, inverted, and smaller
128 Check Your LearningLocate and describe the image in each of the following diagrams:Image is upright, larger, and virtual
129 Check Your LearningImage is inverted, larger, and real.
130 Check Your LearningImage is upright, smaller and virtual
131 Lens Equation Power of a lens defined as If f is in metres, P is in diopters (D)
132 Lens EquationThe object distance do is positive if it is on the same side of the lens from which the light is coming (in other words, if it is real)The image distance di is positive if it is on the opposite side of the lens from which the light is coming (in other words, if it is real); it is negative if it is on the same side of the lens from which the light is coming (in other words, if it is virtual)The height of the image hi is positive if upright and negative if inverted relative to the object.The focal length is positive for a convex (converging) lens and negative for a concave (diverging) lens.
133 Example 3A certain lens focuses an object 22.5 cm away as an image 33.0 cm on the other side of the lens.Is the image real or virtual?What type of lens is it and what is its focal length?What is the power of the lens?
134 SolutionBecause the image is on the other side of the lens, it must be real.Because the image is real, the lens must be convex, or diverging (since concave lenses will always give virtual images). A positive focal length will confirm this.
135 SolutionTo calculate the power, the focal length must be in metres.
136 Check Your LearningA concave lens has a focal point 20.0 cm away from the lens. A 2.1 m tall object is placed 3.0 m away from it.Where is the image?The image is located 0.19 m from the lens on the same side as the object.
137 Check Your Learning How big is the image? Describe the image. The image is upright (because hi is positive), smaller (because hi is smaller than ho), and virtual (because di is negative).
138 Module Summary In this module you learned that Light exhibits many wave properties and can be modeled in many situations as a wave.Light can undergo both regular reflection (mirrors) or diffuse reflection (rough surfaces)Light is just a small part of the electromagnetic spectrum.The speed of light in a vacuum is
139 Module SummaryThe index of refraction for a medium can be calculated usingThe angle of incidence and angle of refraction for a refracting ray of light are related by Snell’s LawWhen going from a high index of refraction to a low index of refraction, there is a critical angle beyond which light cannot refract. For all angles of incidence greater than this critical angle, total internal reflection occurs.
140 Module SummaryDiffraction and interference of light for double slits and diffraction gratings can be modeled using the equationsRay diagrams can be used to locate images in spherical mirrors and lenses.The following equations can be applied to problems involving spherical mirrors and lenses:
141 Module SummaryThe power of a lens can be calculated from the focal length