8.2 &8.3 Notes [Complete]
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Sir Winston Churchill High School**We aren't endorsed by this school
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PHYSICS 20
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Physics
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Dec 16, 2024
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7
Uploaded by ColonelGuineaPig4741
98.2 and 8.3 Superposition and Interference Review Problem: What are the differences between a transverse and a longitudinal wave? Refraction & Reflection Waves often encounter barriers between two wave media. At this barrier, the wave will pass into the new medium andbe partially reflected back into the incident medium. When a wave travels from one medium into another some properties of the wave, including direction, velocity, and wavelength, change. The change in direction of waves in a new medium is called refraction. The wave frequency remains constant when waves change mediums, because it is a property of the wave source and not the wave medium. f1= f2Therefore, we can state: v1λ1=v2λ2andv1v2=λ1λ2where v1and λ1are the wave speed and wavelength in the incident medium and v2and λ2are the wave speed and wavelength in the refracted medium. Example A A wave with a frequency of 2.00 Hz and a wavelength of 10.0 mm travels into a new medium and the wavelength triples. What is the speed of the wave in this new medium? f.=200HIvi=5.7,X,=100mm=YVz=v"2=(2.00Hz)(10.0mm)X,*=30.Omm=20.0mm/s=(20.0mm/s)30.Om10.0m=60.0m/s
10Relative Density of Wave Media Lower Density Medium to Higher Density Medium When a wave pulse travels from a low density to a high density medium: •part of the pulse is reflected back invertedwith the same speedand wavelengthbut lower amplitude•part of the pulse travels through uprightwith reduced speedand wavelengthand lower amplitudeHigher Density Medium to Lower Density Medium When a wave pulse travels from a high density to a low density medium: •part of the pulse is reflected back uprightwith the samespeedand wavelengthbut lower amplitude•part of the pulse travels through uprightwith increasedspeedand wavelengthand lower amplitudeA1’ V1V212A21’ 11222
11Interference & Superposition When two pulses interact in the same space, they will influence one another. This is known as interference. •Constructive Interference: the overlapping pulses create a greater amplitude•Destructive Interference: the overlapping pulses create a lesser amplitudePrinciple of Superposition When two pulses interact, the displacement of the combined pulse at each point of interference is the sumof the displacement of the individual pulses. Constructive Interference The wave pulses approach one another. The wave pulses begin to overlap. The wave pulses fully overlap. The wave pulses move past each other in opposite directions. Destructive Interference The wave pulses approach one another. The wave pulses fully overlap. The wave pulses move past each other in opposite directions.
12Example B Predict where the peak of the interference pulse is located for each scenario below: i.One pulse with a peak 15 cm above the equilibrium line interferes with a pulse with a peak 10 cm above the equilibrium line. ii.One pulse with a peak 16 cm below the equilibrium line interferes with a pulse with a peak 8.0 cm below the equilibrium line. iii.One pulse with a peak 15 cm above the equilibrium line interferes with a pulse with a peak 10 cm below the equilibrium line. iv.One pulse with a peak 15cm above the equilibrium line interferes with a pulse with a peak 15cm below the equilibrium line. Where is the peak of the interference pulse located? Example C The diagram shows two pulses of equal width and height travelling in opposite directions on the same string. Draw the shape of the string when the pulses completely overlap.
13Example D The wave pulses shown in the diagram travel at 1 cm/s and both have width 2 cm. The heights are indicated on the diagram. In each case, draw the shape of the resulting pulse according to the principle of superposition at times t = 0.5 s, t = 1.0 s and t = 1.5 s. Take t = 0 s to be the time when the pulses are about to meet each other. Nodes & Antinodes When two waves combine to create a no amplitude, this is known as a node. When two waves combine to form a maximum amplitude, this is known as an antinode. An interference pattern occurs when two in-phase(same frequency and wavelength) point sources interfere with one another create a series of antinodes, nodes, and everything in-between. The wave fronts of two in-phase point sources (S1and S2) are shown below. "#"$Page 426 in your textbook has a detailed diagram.
14Anti-nodal lines(An): represent the locations where the two waves are exactly in phaseand experience complete constructive interference; and an antinode (maximum) is formed. •Central maximum(A0): equal number of wavelengths from S1and S2to the antinode. •First order maximum (A1): The wave from the further source had to travel 1 complete wavelength further than the wave from the closer source. •Second order maximum (A2): The wave from the further source had to travel 2 complete wavelengths further than the wave from the closer source. Phase shifts equal to whole wavelengths produce maxima (anti-nodal lines). Nodal line(Nn): represents the locations where the two waves are exactly out of phaseand experience complete destructive interference; a node (minimum) is formed. •Zero order minimum (N0): The wave from the further source had to travel 1/2 wavelength further than the wave from the closer source. •First order minimum (N1): The wave from the further source had to travel 3/2 wavelengths further than the wave from the closer source. •Second order minimum (N2): The wave from the further source had to travel 5/2 wavelengths further than the wave from the closer source. Phase shifts equal to an odd number of half wavelengths produce minima (nodal lines).
15Example E In a two in-phase point source interference pattern the distance from one source to an antinode along the line A1is 2.24 m. The distance from the other source to the same antinode is 2.80 m. What is the wavelength of the waves?