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Superposition of Waves Principle of superposition: The displacement of a medium caused by two or more waves is the algebraic sum of each wave. Waves pass each other so the original wave continues unaltered. Interference is the result of the superposition of two or more waves.

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Wave Superposition Constructive Interference 2 or more waves adding together to make a larger wave

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Wave Superposition Destructive Interference Constructive Interference NodesAntinodes The blue wave below represents the sum of the 2 other waves.

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Wave Superposition Student Excel SHM lab plus superposition

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Sound waves travel in all directions Wave front can be created by connecting similar point on the waves

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Double Slit Light Rays

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Double Slit

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Single Slit

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For small angles (θ<15 o )

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Waves at Boundaries Reflected pulse Transmitted pulse Low Density MediumHigh Density Medium Note: Both amplitudes get smaller

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Waves at Boundaries High Density MediumLow Density Medium Reflected pulse Transmitted pulse

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Does the frequency of a wave change as it moves into a new medium? Does the velocity of a wave change as it moves into a new medium? Does the wavelength of a wave change as it moves into a new medium?

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Thin film Interference Soap bubble

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Part of the incident light is reflected on the top surface Part of the light is transmitted and is reflected at the lower surface The lower wave travels the extra distance ABC If the path length ABC is a multiple of λ there will constructive interference Oil Water A B C

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Part of Incident wave is reflected and part is transmitted Reflected wave: from less dense to more dense is reflected 180 degrees out of phase

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In the time it takes the incident wave to travel a distance T (1/4λ), the reflected wave also travels 1/4λ. In the time it takes the transmitted wave to travel back to the original boundary, the reflected wave also travels 1/4 λ

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Identify the phase for wave 1 Inverting or Non-inverting Identify the path length and phase for wave 2 Oil Water A B C

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For constructive interference the phase difference must be a multiple of 2π For destructive interference the phase difference must be an odd multiple of π Oil Water A B C

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A laser shines on a pair of identical glass microscope slides that form a very narrow edge. The waves reflected from the top and the bottom slide interfere. What is the interference pattern from top view?

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As you move closer to the left edge, T goes to zero. What is the phase difference between the two waves at the edge? Destructive interference

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Polarization Sometimes it is desirable to block all but one orientation of incoming light. For instance, you can wear polarizing sun glasses in order to reduce glare. Think “Stars and Bars” in order to understand how polarization works.

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Stars and Bars Imagine you are behind bars. A Ninja comes along and decides to throw stars at you. Are you safe from his stars? As you saw, the first two stars would not hit you. Why? Were you safe from the third star? Why? The first star was horizontally polarized. The second was “other” polarized. Therefore, they could not make it through the vertical bars. The third star was vertically polarized; therefore, it was able to pass through the vertical bars and nail you!

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Cross Polarization Watch the wave below. What is its polarization? Why? Would it be able to pass through if we rotated one polarizer by 90 degrees? Why? Explain what happened.

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Polarization Watch the animations below. Which wave is horizontally polarized? Why? Which one is vertically polarized? Why?

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