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Vibration and Waves

Extra Credit Physics Project

Hayden Mansure

on 28 May 2013

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Transcript of Vibration and Waves

Wave Properties and Interactions Wave Motion Most wave types require a physical medium in order to travel. This means that a wave needs a physical environment through which a disturbance can travel. Waves that require a medium in order to travel are known as mechanical waves. Question If sound waves are considered mechanical, then why is it impossible for sound to travel through space? Medium Longitudinal Waves When the particles of the medium vibrate parallel to the direction of a wave motion the wave is called a longitudinal wave. Longitudinal waves can also be described by a sine curve. How are sound waves in the air longitudinal waves? Parts of a Wave Wave measures include crest, trough, amplitude, and wavelength Properties of Waves A wave is the motion of a disturbance. The disturbance causes water on the surface near the point to move, which causes points farther away to move. Waves travel outward in a circular pattern away from the original disturbance. Wave Types A wave that consists of a pulse is called a pulse wave. A physical environment through which a disturbance can travel is called the medium. Waves of almost every kind require a material medium in which to travel. Waves that require a material medium are known as mechanical waves. Space is nearly a vacuum. In order for sound waves to travel they must have a medium such as air or water. A periodic wave occurs when the source of the wave's motion is periodic. - A wave whose source vibrates with simple harmonic motion is called a sine wave. A sine wave is a special case of periodic wave due to it's simple harmonic vibration pattern. Transverse Waves A wave whose particles vibrate perpendicularly to the direction the wave is traveling is called a transverse wave. Vibrations of a transverse wave are perpendicular to the wave motion. A waveform can represent either the displacements of each point of the wave at a single moment in t (time) or the displacements of a single particle as time passes. The x-axis represents the equilibrium position and the y-axis represents the displacement. At the highest and lowest points of the curve, where displacement is greatest, the absolute values of y are greatest. A wave can be measured in terms of its displacement from equilibrium. The highest point above equilibrium position is called the wave crest. The lowest point is called the trough. The amplitude is a measure of maximum displacement from equilibrium. The amplitude of a wave is measured from the displacement down to the trough, or up to the crest. The distance a wave travels along its path during one cycle is called the wavelength. Wavelength is represented by the Greek symbol lambda To measure the wavelength measure the length from crest to crest or trough to trough. Air particles vibrate back and forth in a direction parallel to the direction of wave motion making it a longitudinal wave. Period, Frequency, and Wave Speed Wave frequency describes the number of waves that pass a given point in a unit of time. The period of a wave is the time required for one complete cycle of vibration of the medium's particles. The period of a wave describes the time it takes for a complete wavelength to pass a given point.
Period and frequency, as in simple harmonic motion, is still inversely related. Wave speed equals frequency times wavelength. The speed of a mechanical wave is constant. When a mechanical wave's frequency increases its wavelength must decrease in order for its speed to remain constant. The speed of the wave changes only when the wave moves from one medium to another when certain properties of the medium are varied. For an example temperature. Waves transfer energy Waves transfer energy by the vibration of matter rather than by the transfer of matter itself. The rate at which a wave transfers energy depends on the amplitude at which the particles of the medium are vibrating. The greater the amplitude the more energy a wave carries in a given time interval. For a mechanical wave, the energy transferred is proportional to the square of the wave's amplitude. What happens when the amplitude of a mechanical wave is doubled What about halved? The time interval increases by a factor of four. When doubled and the energy decreases by a factor of four when halved. Wave Interactions Since mechanical waves are not matter but rather displacements of matter two waves can occupy the same space at the same time. The combination of two overlapping waves is called superposition. Visible light and other forms of electromagnetic radiation also undergo superposition, and they can interact to form interference patterns. Superposition Principle When two or more waves travel through a medium at the same time, the resultant wave is the sum of the displacements of the individual waves at each point. Superposition principle is only valid when the individual waves have small amplitudes. Each wave contains its own characteristics after interference. Constructive interference A superposition of two or more waves in which individual displacements on the same side of the equilibrium position are added together to form the resultant wave. Displacement in the same direction produces a constructive interference. Destructive Interference A superposition of two or more waves in which individual displacements on opposite sides of the equilibrium position are added together to form the resultant wave Displacement of opposite directions produce destructive interference. Complete destructive interference occurs when two pulses overlap and cancel When a wave is going through compression, particles move closer together, but while in rarefaction particles are spread farther apart. When a compression or a rarefaction occur there is a destructive interference. Reflection At a free boundary, waves are reflected. At a fixed boundary, waves are reflected and inverted. Standing Waves A wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere. Standing waves have nodes and anti nodes. The points at which complete destructive interference happens are called nodes. An anti node is the point in a standing wave, halfway between two nodes at which the largest displacement occurs. What you should have learned As a wave travels, the particles of the medium vibrate around an equillibrium position.
In a transverse wave, vibrations are perpendicular to the direction of wave motion. In a longitudinal wave, vibrations are parallel to the direction of motion.
Wave speed equals frequency times wavelength. If two or more waves are moving through a medium, the resultant wave is found by adding the individual displacements together point by point.
Standing waves are formed when two waves that have the same frequency, amplitude and wavelength travel in the opposite directions and interfere.
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