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Vibration and Waves
Transcript of Vibration and Waves
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.