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VIBRATIONS AND WAVES. Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law. Harmonic Motion Oscillator.
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Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law.
Harmonic Motion Oscillator http://www.kettering.edu/~drussell/Demos/SHO/mass.html
Energy Conversion http://www.kettering.edu/~drussell/Demos/SHO/mass.html
Simple Harmonic Motion (SHM) • Motion that occurs when the restoring force acting on an object is proportional to the object’s displacement from its resting position • Harmonic part if SHM means the motion repeats itself • Objects at the end of springs move in SHM when they are displaced from their rest position and bounce up and down on the spring, or oscillate.
Sine Curve • To and fro vibration motion of swinging pendulum in small arc is called SHM
Sine Curve • Pictorial representation of a wave
VIBRATION OF A PENDULUM • What does the period (T) depend upon? • Length of the pendulum (l). • Acceleration due to gravity (g). • Period does not depend upon the bob mass.
Pendulum When oscillations are small, the motion is called simple harmonic motion (SHM) and can be described by a simple sine curve.
WAVES • Transfer energy not matter from one place to another • Disturbance that moves through space or through a medium (material)
There are two ways to transmit information/energy in our universe: Particle Motion and Wave Motion Wave Simulation: http://phet.colorado.edu/simulations/sims.php?sim=Wave_Interference
Mechanical Waves • Requires a medium • Ex. Water waves, sound • Two different material objects cannot be in the same place at the same time…however mechanical waves displace matter to transfer energy and thus can be in the same place at the same time.
Electromagnetic Waves • Do not require a medium (can move through empty space, a vacuum) • Ex. Radio waves, light waves, microwaves
Wave Pulse • Single Disturbance http://www.colorado.edu/physics/phys4830/phys4830_fa01/lab/n0911.htm
Wave Train (Continuous Wave) • Series of pulses at regular intervals
Particles vibrate perpendicular to the wave motion Transverse waves can be polarized string musical instruments ripples on water electromagnetic waves e.g. Light waves, x-rays, radio waves TRANSVERSE WAVES
Picture of a Transverse Wave Crest l Wavelength A A - Amplitude Trough
Transverse Wave • http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xml
Longitudinal Wave • Particles vibrate parallel to the direction of wave travel • Ex. Sound
LONGITUDINAL WAVES Particles vibrate parallel to the motion of the waves Ex: Sound Waves • http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xml
Rarefactionsare regions of low density. Compressions (condensations) are regions of high density. lis the length of one rarefaction plus one compression Animated comparison of transverse & longitudinal waves: http://members.aol.com/nicholashl/waves/movingwaves.html
Period (T) Time required to make one vibration. • Time required to generate one wave • Time required for the wave to travel one wavelength.
The number of vibrations per unit of time made by the vibrating source. Units -cycles/sec or hertz (Hz) Frequency (f)
Examples of Frequency • What is the frequency of the second hand of a clock? Frequency = 1cycle/60 sec Period = 60 sec • What is the frequency of US Presidential elections? Frequency = 1 election/4 yrs Period = 4 yrs
WAVE SPEED The average speed is defined as
For a wave, if the distance traveled is a wavelength (l), then the time to travel this distance is the period (T). Thus or
is true for all waves. Note: v is determined by the medium. f is dictated by the source.
Surface Water Waves • http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xml
Superposition Two or more waves overlapping in some way The overlapping causes interference Animation courtesy of Dr. Dan Russell, Kettering University
Wave Interactions • Because waves are not matter but rather displacement of matter, two waves can occupy the same space at the same time • Combination of two overlapping waves is called superposition (causes interference)
Superposition Principle • Displacement of a medium (material) caused by 2 or more waves is the sum of the displacements of the individual waves at each point • Holds true for all types of waves
Interference • Interference is a characteristic of all waves. • Result of superposition of 2 or more waves • Constructive- (crest meets crest or trough meets trough) amplitudes added • Destructive- (crest meets trough) amplitudes subtract
Constructive Interference Reinforcement†Maximum In phase displacement
Constructive Interference • When the crest of one wave overlaps the crest of another
Destructive- Crests and Troughs overlap CANCELLATION Zero Displacement
Interference –Destructive • When the crest of one wave overlaps the trough of another
Standing Waves • When two sets of waves of equal amplitude and wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is “standing still.”
Standing Wave Incident Wave V Reflected Wave V V Standing Wave V
Standing Waves • Result of interference and reflection • When 2 sets of waves of equal amplitude and λ pass through each other in opposite directions, the waves are steadily in and out of phase with each other. • Consists of nodes (0 amplitude) and antinodes (max. amplitude) • Wave looks as if it is standing still
Standing Waves • Nodes- point in standing wave that undergoes complete deconstructive interference and is therefore stationary (no vibration) • Antinode- a point in a standing wave (1/2way between 2 nodes) at which the largest amplitude occurs (maximum vibration) Waves on a String: http://phet.colorado.edu/simulations/sims.php?sim=Wave_on_a_String
Standing Waves • Since the two identical waves travel in opposite directions, the net energy flow is zero; the energy is “standing” in the loops
There is maximum vibration at an antinode. There is no vibration at a node. l