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Properties of Waves and Wave Interactions Mark Lesmeister Pearland ISD Physics Some physics graphics © Copyright 2002 Holt Rinehart and Winston

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PART 1: INTRODUCTION TO WAVES

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Definition of Waves A wave is the motion of a disturbance of some physical quantity. A wave transfers energy without a large-scale transfer of matter.

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Waveform diagram A wave can be represented with a waveform diagram. A waveform diagram shows the position of each point of the medium at a moment in time, or the position of a single point over time. © Copyright 2002 Holt Rinehart and Winston

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PART 2: TYPES OF WAVES

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Mechanical & Nonmechanical Waves Mechanical waves require a material medium. Examples are: Sound waves Water waves Shock waves in an explosion Other waves, such as electromagnetic waves, do not require a material medium. Examples are: Light X-rays Radio waves

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Pulse Waves and Periodic Waves Pulse wave- a wave which consists of a single, non-repeated disturbance or pulse. Animation courtesy of Dr. Dan Russell, Kettering University

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Pulse Waves and Periodic Waves Periodic wave- a wave whose source is some form of periodic motion. Animation courtesy of Dr. Dan Russell, Kettering University

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Sinusoidal Waves A periodic wave whose source vibrates with simple harmonic motion produces a sinusoidal wave. This is a wave whose graph is shaped like a sine or cosine graph.

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Quick-lab 1: Types of Waves Using the thin coiled spring, send a single pulse down the spring as demonstrated by your instructor. In which direction was the wave energy moving? In which direction(s) did the spring move? Using the slinky spring, send a single pulse down the spring, as demonstrated by your instructor. In which direction was the wave energy moving? In which direction did the spring move?

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Transverse and Longitudinal Waves Transverse wave – a wave whose particles vibrate perpendicular to the direction of travel of the wave. Examples include: Surface waves on water. Electromagnetic waves Animation courtesy of Dr. Dan Russell, Kettering University

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Transverse and Longitudinal Waves Longitudinal wave- a wave whose particles vibrate parallel to the direction of travel of the wave. Examples include: Sound waves Compression waves in explosions. Animation courtesy of Dr. Dan Russell, Kettering University

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Transverse Wave A transverse wave has crests and troughs. © Copyright 2002 Holt Rinehart and Winston

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Longitudinal Waves Longitudinal waves are sometimes referred to as density waves. They can be represented by the same waveforms as transverse waves. © Copyright 2002 Holt Rinehart and Winston

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PART 2: CHARACTERISTICS OF WAVES

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Frequency and Period Frequency – the number of crests (or troughs) passing a reference point per second. Frequency Frequency is measure in cycles/second 1 Cycle/second = 1 s -1 = 1 Hertz Period – the time between the passage of two successive wave crests (or troughs) past a reference point. The period is a time interval, so it is measured in seconds. The frequency is the reciprocal of the period. We also say frequency and period are inversely related.

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Wavelength wavelength ( ) – distance between two adjacent similar points of the wave, such as from crest to crest or trough to trough It is also the distance advanced by the wave motion in one period. © Copyright 2002 Holt Rinehart and Winston

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Quick Lab 2: Wave Speed Using the coiled spring to send transverse pulse waves. Using the stopwatch, time how long it takes for the pulse to travel the length of the spring. Try timing the speed of pulses with different amplitudes.

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Wave Speed Wave speed: The speed of the moving disturbance. v = f

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Quick Lab 3: Wave Equation Using the coiled spring to make transverse waves. Change the frequency of the waves and observe what happens to the wavelength.

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Wave Speed Practice Problem A tuning fork produces a sound with a frequency of 256 Hz and a wavelength in air of 1.35 meters. What is the speed of sound in air? Answer: v = 346 m/s

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Amplitude amplitude – the maximum displacement of the vibrating particles of the medium from their equilibrium positions. The amplitude of a wave is related to the energy transported by the wave. © Copyright 2002 Holt Rinehart and Winston

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Power and damping power- the rate of transfer of energy by a wave. The power of a wave is proportional to the square of the wave amplitude and also to the square of the wave frequency damping – the reduction in amplitude of a wave due to the dissipation of wave energy as it travels away from the source.

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PART 4: INTERACTIONS OF WAVES

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Quick Lab 4: Wave Interactions Using the Slinky ® or the thin coil spring, have students on both end of the spring launch pulses as the same time. Experiment with what happens when two pulses meet in the middle of the spring.

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Superposition superposition – the combination of two overlapping waves. When waves overlap, the displacements of the waves at each point are added to find the resultant displacement. Animation courtesy of Dr. Dan Russell, Kettering University

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Constructive Interference constructive interference – when individual displacements on the same side of the equilibrium position are added together to form the resultant wave. The resultant displacement is larger than either of the component displacements.

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Constructive Interference © Copyright 2002 Holt Rinehart and Winston

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Destructive Interference destructive interference – when individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave. The resultant is smaller than at least one of the component displacements.

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Destructive Interference © Copyright 2002 Holt Rinehart and Winston

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Interference Patterns Waves that meet form interference patterns.interference patterns.

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Wave Reflection reflection- the turning-back of a wave when it strikes a boundary.

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Wave Reflection at a Fixed Boundary At a fixed boundary, waves are reflected and inverted. Animation courtesy of Dr. Dan Russell, Kettering University

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Wave Reflection at a Free Boundary At a free boundary, waves are reflected upright. Animation courtesy of Dr. Dan Russell, Kettering University

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Wave Reflection © Copyright 2002 Holt Rinehart and Winston

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Quick Lab 5: Standing waves As demonstrated by your instructor, shake the spring with a gradually increasing frequency, and observe what happens at certain fast enough frequencies.

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Standing Waves standing wave – a wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere. Animation courtesy of Dr. Dan Russell, Kettering University

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Standing Waves node – a point in a standing wave that always undergoes complete destructive interference and therefore is stationary. antinode – a point in a standing wave, halfway between two nodes, at which the largest amplitude occurs.

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Standing Waves © Copyright 2002 Holt Rinehart and Winston

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Types of Waves: De Broglie Waves

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