Waves & Energy Transfer. Introduction to Waves. Waves are all about Periodic Motion. Physics 11. Chapter 11 ( 11-1, 11-7, 11-8)

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1 Waves & Energy Transfer Physics 11 Introduction to Waves Chapter 11 ( 11-1, 11-7, 11-8) Waves are all about Periodic Motion. Periodic motion is motion that repeats after a certain period of time. This time is appropriately known as the period, T. Crest Trough Time

2 Frequency This is the number of oscillations per second. It is related to the Period 1 Frequency = Period 1 f = T Frequency is measured in Hertz (Hz) 1 15 Hz =15 If you hear Hertz, think per second s Quick Example A pendulum has a period of 0.25s, what is it s frequency? f = = = = Hz T 0.25s 0.25 s 4 4Hz so think 4 per second This makes sense, because if it takes ¼ of a second to make one oscillation, it will do 4 in one second. Common places to use Frequency Computer processors the Pentium 4 operates at 3.8 GHz (calculations per second) Digital music and video The audio file was encoded at 128 khz Heart rate his heart rate was 80bpm Beats per minute (1/time)

3 Amplitude The Amplitude, A, of a wave describes how much the wave deviates from it s equilibrium/average position (math class, the sinusoidal axis) Time Types of Waves Sound Waves -a longitudinal wave Light (EM) Waves

4 Mechanical Waves So far we have only dealt with things that oscillate in time. Waves can exist in substances too Disturbances of this sort are referred to as Mechanical Waves Water waves Sound waves Waves in springs You may be wondering about Light.. Light is a wave too, but it doesn t travel though any stuff Originally they thought it must go through something, and they called this stuff ether They looked for evidence of this ether, but were unable to find evidence of it. Michelson-Morley Experiment Not mechanical in the sense the other disturbances are. has many of the same properties Electromagnetic (EM) Waves ( 22-5, 24-4) Those that consist of oscillating electric and magnetic fields that move at the speed of light or c through space Examples: visible light, radio and x-rays Do not require a medium for transmission

5 Electromagnetic (EM) Waves Frequencies of EM waves are displayed on the EM spectrum: Electromagnetic (EM) Waves visible light of different wavelengths perceived as colors (R-O-Y-G-B-I-V) Electromagnetic (EM) Waves Individual wavelengths can be observed using a diffraction grating

6 Matter Waves Wave-like behavior of particles, such as electrons Use quantum mechanics to describe it Electron diffraction pattern Properties of Waves Period T, still exists The period is how long it takes a for one spot along the wave to see a crest after it saw the last one Frequency, f, still defined the same way Wavelength, λ, a new quantity. Distance from crest to crest (or trough to trough) λ, T

7 Do waves move? There is nothing physical that moves from one point to another The disturbance does travel The Universal Wave Equation: v = fλ λ, T Practice Questions 1. A metronome beats 54 times over a 55 s time interval. Determine the frequency and period of its motion. 2. A child swings back and forth on a swing 12 times in 30.0 s. Determine the frequency and period of the swinging. Practice Questions 3. The speed of sound in air at room temperature is 343 m/s. The sound wave produced by striking middle C on a piano has a frequency of 256 Hz. a. Calculate the wavelength of this sound. b. Calculate the wavelength for the sound produced by high C, one octave higher than middle C, with a frequency of 512 Hz.

8 Practice Questions 4. Interstellar (a.k.a. between the stars ) hydrogen gas emits radio waves with a wavelength of 21 cm. Given that radio waves travel at 3.0 x 10 8 m/s, what is the frequency of this interstellar source of radiation? Reflection and Transmission Chapter 11 ( 11-11) Waves at Boundaries When a wave moves from one medium to another, its frequency remains the same but the speed changes As the speed is related to the properties of the medium, the behaviour will depend on the media involved The behaviour at the boundary will depend on whether the wave is travelling from a less dense medium to a more dense medium or vice versa

9 Waves at Boundaries an incident wave reaches a boundary between 2 media part of incident wave continues on in new medium with same frequency transmitted wave part of wave moves backward from boundary in old medium reflected wave if difference in media is small, amplitude of transmitted wave will be almost as big as incident wave & amplitude of reflected wave will be relatively small (most of energy transmitted) if 2 media densities are very different, most of energy will be reflected Less Dense to More Dense Boundary Whenever wave passes from less dense to more dense medium, reflected wave is inverted More Dense to Less Dense Boundary Whenever wave passes from more dense to less dense medium, reflected wave is erect, not inverted Video 1 Video 2

10 Wave Interference Chapter 11 ( 11-11, 11-12) Wave Superposition Principle of Superposition states: "the displacement of a medium caused by two or more waves is the algebraic sum of the displacements caused by individual waves" result of superposition is interference Wave Superposition Constructive interference occurs when amplitudes are in same direction result is wave with larger amplitude than any individual wave

11 Wave Superposition Destructive interference occurs when amplitudes are in opposite direction as 2 pulses overlap, displacement is reduced Standing Waves waves are able to pass through one another unchanged 2 pulses with equal but opposite displacements meet (destructive interference) find one point that is undisturbed node 2 pulses with equal displacements in the same direction meet (constructive interference) find point of maximum amplitude antinode wave in which nodes and antinodes are stationary standing wave Fixed Both Ends Nodes at either end 1 st harmonic is half a wavelength, with an anti-node (maxima) in the middle 2 nd harmonic is one wavelength with a node in the middle and maxima between nodes

12 Fixed One End ( 12-5) Generally seen in sound waves 1 st harmonic is one quarter of a wavelength with a node and maxima 2 nd harmonic is 3/4 s of a wavelength with two nodes and two maxima Guitar String A guitar string has a given (open) length, given tension (and therefore mostly constant wave speed in a string) and therefore, when a string is plucked, a specific frequency is heard If the string is then shortened by a certain amount, a higher frequency can be played Superposition and Spectra Physics 11

13 Multiple waves We now understand the very basics of waves but reality usually does not involve one just one wave. Multiple radio stations transmitting into the room Waves on the surface of a pool as people are jumping in White light (it is a composite of waves in the EM spectrum) So what doe these waves look like? Superposition Superimpose two waves together. Add them together For each value of x, add the value of each wave to get a resultant Real Waves are Superpositions This means that real waves have a number of waves adding together to make them up. Each part having a different wavelength The wavelengths that are used to construct a complex wave are referred to as a Spectrum (plural, Spectra )

14 Spectrum Graphs Real waves are composed of many components To keep track of what wavelengths are used, a simple chart is often made. Consider the emission spectrum of Hydrogen It tells us what wavelengths are present, indicating the wavelength qualitatively with the color of light Hydrogen

15 How are spectra formed at the atomic level? Intensity Spectra Spectra plots can include information about amplitude at each wavelength Consider these plots made for common white light or WL sources Various WL sources Relitive intensity (arb units) solar 1 incandecent bulb flouresent blub lcd white crt white Wavelength (nm) Wave Behaviour Physics 11

16 Diffraction ( 11-13, 24-6) When a wave impinges on a single opening, it will diffract That is, a plane wave will spread through space and the spreading angle is a function of wavelength and opening Single Slit Diffraction If light is impingent on a single slit, the light wave will spread The spreading angle is related to the size of the opening and the wavelength of light used Two Point Sources Two point sources will also interfere to create an interference pattern The interference pattern is based on wavelength and separation of point sources

17 Young s Double- Slit Experiment ( 24-3) If light is impingent on two slits, the light will spread from each slit like in the single slit case However, the waves will interfere with each other and an interference pattern will result Diffraction Gratings A diffraction grating combines the behaviour of a single slit and double slit and is created by creating many grooves or slits on a transparent or reflective material Diffraction Grating These examples of diffraction gratings have many grooves (or slits) and as a result, separates light into its constitute wavelengths (colours)

18 Doppler Effect ( 12-8, 12-9) When an source is moving with respect to an observer (or vice versa) the frequency of the sound will shift due to the Doppler Effect As a result, it is possible to determine whether an object is moving toward or away from us if we know the reference frequency Doppler Effect Doppler Effect For sound As a sound source moves towards the observer or receiver, the frequency or pitch increases As the sound source moves away from the receiver, the frequency decreases

19 Sonic Boom A sonic boom is the sound associated with the shock waves created by an object traveling through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding much like an explosion. Ex: supersonic jets, cracking of a whip, pop of a balloon For light We can see the same behaviour with light; since light (in a vacuum) must always travel at the speed of light (3.0x10 8 m/s) However, since nothing can travel faster than the speed of light (in a vacuum) it is impossible to see behaviour akin to a sonic boom with light (in a vacuum) Red and Blue Shift When the wavelength or frequency of light is changed, so is its colour For visible light, this means that when an emitter is moving away from Earth, the wavelength observed is increased and light is said to be red shifted When light is emitter by a body moving toward Earth, wavelength is decreased and we say that it is blue shifted Ex: rotation of galaxies; Hubble s expansion of Universe

20 Cerenkov Radiation Cerenkov radiation is EM radiation emitted when a charged particle (such as an electron) passes through a medium at a speed greater than the speed of light in that medium. Ex: blue light from nuclear reactor Reflection ( 11-11, 23-2) According to ray optics, reflection can be modelled using a ray impingent on a mirror at some angle and reflected at the same angle θ i = θ r Refraction ( 11-13, 23-4, 23-5, 23-6) Refraction is the change in direction or bending of light at boundary between 2 media Optically Dense - when speed of light in one medium is slower than that in another when angle of incidence = 0 o, angle of refraction = 0 o speed changes but passes straight through, along the normal when light travels into a medium where it travels faster, angle of refraction > angle of incidence OR if light enters less optically dense medium, refracted rays bend away from the normal if light enters more optically dense medium, refracted rays bend toward the normal Index of Refraction (n) - ratio of the speed of light in a vacuum to its speed into a material n = s c v s

21 Refraction Light bends inward when entering medium of higher index of refraction Light bends outward when entering medium of lower index of refraction Snell s Law Light moving from smaller n to larger n is bent toward normal & vice-versa n i is index of refraction for incident medium n r is index of refraction for second medium are angles of incidence & refraction refractive index (n) can be found by measuring angles of incidence & refraction Critical Angle Critical Angle (θ c ) occurs when the refracted ray lies along the boundary of the medium surface

22 Total Internal Reflection Total Internal Reflection occurs when light passes from a more optically dense medium to a less optically dense one at an angle so great that there is no refracted ray Ex: fiber optic cable, internal body probe