Transcript Vibrations and Waves. So much fun, you can’t stand it!
Vibrations and Waves. So much fun, you can’t stand it!
First rule of leadership: everything is your fault.
She wrote me a 'john-deere' letter... something about me not listening enough, I don't know... I wasn't really paying attention.
Take a pendulum, guitar string, weight bobbing on a spring, all of these objects have a motion that repeats in cycles, and all are examples of
periodic motion.
If the force that restores the object to its equilibrium position is directly proportional to the displacement of the object is it in
simple harmonic motion.
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Two properties describe something that is in simple harmonic motion,
period and amplitude.
Period
, is the time it takes for one complete cycle of a wave or periodic motion.
Amplitude,
is the greatest displacement from rest
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Springs can exhibit periodic motion because the force exerted by the spring is directly proportional to the distance it is stretched multiplied by a spring constant specific to the type of spring.
This is known as Hooke’s Law F=-kx F = force, k = spring constant, x = distance
You've got to ask yourself one question: 'Do I feel lucky?' Well, do ya, punk?
Most springs obey this law, but not all.
If I graph Force versus distance with regard to a spring the slope of the graph is equal to the spring constant and the area under the graph is equal to the work done by the spring.
Potential energy in a spring is equal to PE = ½ kx 2
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The period of oscillation of a spring depends on the mass of the object and the strength of the spring. T = 2 The period of a pendulum is a function of the length of the rod or string and gravity and looks like this: T = 2 l/g
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Resonance, occurs when small forces are applied at regular intervals to a vibrating or oscillating object and the amplitude or vibration increases The addition of small forces at specific times increases the amplitude Pushing a stuck car, trampoline, diving board etc.
Resonance can be very destructive to structures.
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A wave is a disturbance that carries energy through matter or space. It does not carry matter.
Mechanical waves are waves that need a medium to travel.
Electromagnetic waves do not.
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There are 3 types of mechanical waves.
Transverse waves displace matter perpendicular to the direction of wave motion. (think rope, sine curve, etc) Longitudinal (compressional) waves displace matter parallel or inline with the direction of the wave. ( Think slinky, earthquake)
I feel the need -- the need for speed!
Surface waves, aka water waves are a combination of both transverse and longitudinal.
Water particles are displaced both perpendicular and longitudinal to the wave direction
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Wave properties include speed, amplitude, crest, trough, wavelength, frequency, period, phase.
Speed is a function of delta d/ delta t Amplitude is the greatest displacement from rest, greater amplitude, greater energy.
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Energy transferred is equal to the amplitude squared.
For waves at the same speed, doubling the amplitude increases the amount of energy it transfers by a factor of 4 Crest is the high point of the wave Trough is the low point
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In a longitudinal wave, compression and rarefaction are synonymous with crest and trough.
Wavelength is equal to one complete wave cycle or any two equal points on the wave, crest to crest, trough to trough. Represented by the Greek letter lambda
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Frequency is the number of complete oscillations per second and is also the inverse of the period of the wave.
f = 1/T Frequency is measureed in hertz, 1 cycle/second Wavelength is equal to velocity divided by frequency Wavelength = v/f Phase is one waves relation to another
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The speed of a wave depends on the medium it travels through, not the amplitude or frequency. Sound waves for example travel slower in colder air than warm air, light travels slower through glass than through air.
When waves strike a barrier the incoming wave is the incident wave the outgoing wave is the reflected wave.
Super Long Slinky in the Hall
The reflected wave off of a more dense object will be the inverse, same magnitude.
The reflected wave off of something less dense will the same phase but with less magnitude, the rest of the wave is carried in onto the other medium.
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The principle of superposition states that the displacement of a medium by two or more waves is the algebraic sum of the displacement of the individual waves.
Waves can either have constructive interference or destructive interference. When waves cancel and result in no displacement, this is called a node.
When waves build and result in increased displacement this is called an antinode.
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A standing wave is one that appears to be still with nodes at one end and the antinode in the middle. Doubling the frequency produces one more node and antinode.
I didn’t get this job by being in the 75
th
percentile
When waves reflect off of a boundary the angle of incidence equals the angle of reflection from the normal (an imaginary line drawn perpendicular from the boundary) Refraction is the bending or slowing of a wave as it passes from one medium to another.
A wave front represents the crest of a wave in two dimensions