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1 Compiled by: Syed Muhammad Irtiqa – Yr.12A :) Chapter(s) Notes: Frequency, Wavelength and Speed:- Any part of the electromagnetic spectrum has a frequency that decides what type of wave it is. This frequency does not change when the wave is refracted. If the speed of the wave is reduced the wavelength of the wave must therefore also be reduced as: Speed = frequency x wavelength (v= f λ) So the wavelength of blue light in air will be slightly longer than the wavelength of blue light in glass! To calculate frequency from time period of wave (Time taken for wave to complete one whole oscillation), use the formula: f = 1/T General Wave Properties:-
- Displacement (x) of a wave is the distance from its equilibrium position. It is a vector quantity; it can be positive or negative.
- Amplitude (A) is the maximum displacement of a particle in the wave from its equilibrium position.
- Wavelength (λ) is the distance between points on successive oscillations of the wave that are in phase.
- All of the above are measured in metres (m).
- Period (T) or time period, is the time taken for one complete oscillation or cycle of the wave. Measured in seconds (s).
- Frequency (f) is the number of complete oscillations per unit time. Measured in Hertz (Hz) or s-
- Speed (v) is the distance travelled by the wave per unit time. Measured in metres per second (m s-1).
2 Phase:- The phase difference tells us how much a point or a wave is in front or behind another. This can be found from the relative positive of the crests or troughs of two different waves of the same frequency. When the crests or troughs are aligned, the waves are in phase. When the crest of one wave aligns with the trough of another, they are in antiphase. The formula for finding phase difference is: Tip: 180 O^ = π radian 360 O^ = 2π radians 540 O^ = 3π radians …. and so on
4 Wave Intensity:- Progressive waves transfer energy. The amount of energy passing through a unit area per unit time is the intensity of the wave. Therefore, the intensity is defined as power per unit area. The area the wave passes through is perpendicular to the direction of its velocity. The intensity of a progressive wave is also proportional to its amplitude squared and frequency squared.
5 w Transverse and Longitudinal waves:- In mechanical waves, particles oscillate about fixed points. The direction of oscillations with regards to the direction of wave travel determine what type of wave it is. A transverse wave is one where the particles oscillate perpendicular to the direction of the wave travel (and energy transfer). Transverse waves show areas of crests (peaks) and troughs. Examples of transverse waves are: Electromagnetic waves e.g. radio, visible light, UV. Vibrations on a guitar string. A longitudinal wave is one where the particles oscillate parallel to the direction of the wave travel (and energy transfer). Longitudinal waves show areas of compressions and rarefactions. Examples of longitudinal waves are: Sound waves. Ultrasound waves.
7 Notice how the waves are closer together between the source and the observer compared to point P and the source. This also works if the source is moving away from the observer. If the observer was at point P instead, they would hear the sound at a lower frequency due to the wavelength of the waves broadening. The frequency is increased when the source is moving towards the observer. The frequency is decreased when the source is moving away from the observer. Calculating Doppler Shift:- When a source of sound waves moves relative to a stationary observer, the observed frequency can be calculated using the equation below: The wave velocity for sound waves is 340 ms-1. The ± depends on whether the source is moving towards or away from the observer. If the source is moving towards, the denominator is v - vs If the source is moving away, the denominator is v + vs
8 Properties of Electromagnetic Waves:- Visible light is just one part of a much bigger spectrum: The Electromagnetic Spectrum. All electromagnetic waves have the following properties in common: They are all transverse waves. They can all travel in a vacuum. They all travel at the same speed in a vacuum (free space) — the speed of light 3 × 10^8 ms- .
10 Malus's Law:- The intensity of unpolarised light is reduced as a result of polarization. If unpolarised light of intensity I 0 passes through a polariser, the intensity of the transmitted polarised light falls by a half. The first filter that the unpolarised light goes through is the polarizer. A second filter placed after the first one is known as an analyser. If the analyser has the same orientation as the polariser, the light transmitted by the analyser has the same intensity as the light incident on it. If they have a different orientation, we must used Malus's law. Malus's law states that if the analyser is rotated by an angle θ with respect to the polariser, the intensity of the light transmitted by the analyser is:
11 The Principle of Superposition:- The principle of superposition states that when two or more waves with the same frequency travelling in opposite directions overlap, the resultant displacement is the sum of displacements of each wave. This principle describes how waves which meet at a point in space interact. When two waves with the same frequency and amplitude arrive at a point, they superpose either: in phase, causing constructive interference. The peaks and troughs line up on both waves. The resultant wave has double the amplitude. or, in anti-phase, causing destructive interference. The peaks on one wave line up with the troughs of the other. The resultant wave has no amplitude. Two sources are coherent when they emit waves with a constant phase difference
13 What is Diffraction? Diffraction is the spreading out of waves when they pass an obstruction. This obstruction is typically a narrow slit (an aperture). The extent of diffraction depends on the width of the gap compared with the wavelength of the waves. Diffraction is the most prominent when the width of the slit is approximately equal to the wavelength. Diffraction is usually represented by a wavefront as shown by the vertical lines in the diagram above. The only property of a wave that changes when it’s diffracted is its amplitude. This is because some energy is dissipated when a wave is diffracted through a gap. Diffraction can also occur when waves curve around an edge. The effects of diffraction are most prominent when the gap size is approximately the same or smaller than the wavelength of the wave. As the gap size increases, the effect gradually gets less pronounced until, in the case that the gap is much larger than the wavelength, the waves are no longer spread out. Double Slit Interference:- Young’s double slit experiment demonstrates how light waves produced an interference pattern. The experiment is shown below (see next page).
14 x (distance between adjacent minima) When a monochromatic light source is placed behind a single slit, the light is diffracted producing two light sources at the double slits A and B. Since both light sources originate from the same primary source, they are coherent and will therefore create an observable interference pattern. Both diffracted light from the double slits create an interference pattern made up of bright and dark fringes. The wavelength of the light can be calculated from the interference pattern and experiment set up. These are related using the double-slit equation. If width of each slit is increased but the separation between the slits remain constant, fringe spacing remains same while brightness of bright fringes increases but change on the dark fringes. When the separation of the slits is increased, there will be no change on the brightness but fringe spacing will decrease. where:- λ = wavelength (m) a = slit separation x = distance between adjacent maxima or minima d = distance between double slit to screen x (distance between adjacent maxima) a d
16 If the incident light is not monochromatic, for instance a white light, the diffraction grating will disperse the light into its component wavelengths. Colors from which white light is made will bend at different angles. Red colour will bend most because it has the longest wavelength out of all the colors. The equation for diffraction grating: Exam questions sometime state the lines per m (or per mm, per nm etc.) on the grating which is represented by the symbol N. d can be calculated from N using the equation.
17 Angular Separation:- The angular separation of each maxima is calculated by rearranging the grating equation to make θ the subject. The angle θ is taken from the centre meaning the higher orders are at greater angles. The angular separation between two angles is found by subtracting the smaller angle from the larger one. The angular separation between the first and second maxima n 1 and n 2 is θ 2 – θ 1 The maximum angle to see orders of maxima is when the beam is at right angles to the diffraction grating. This means θ = 90o^ and sin θ = 1. The highest order of maxima visible is therefore calculated by the equation: Note that since n must be an integer, if the value is a decimal it must be rounded down. E.g If n is calculated as 2.7 then n = 2 is the highest order visible.
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20 Fig. 6.1 shows wavefronts incident on, and emerging from, a double slit arrangement. The wavefronts represent successive crests of the wave. The line OX shows one direction along which constructive interference may be observed.
