Ch+13+-+Oscillations+and+Waves

Waves transfer energy Moves from mechanical model(springs) of simple harmonic motion to waves

Hooke's Law F=-kx k = spring constant and it is negative because the force is opposite the displacement

Restoring Force always pulls the object toward the equilibrium position (x=00

Simple Harmonic Motion(SHM) SHM occurs when the net force in the direction of the motion is a Hooke's Law type of force Force is proportional to displacement and in the opposite direction

SHM in Springs and Waves Amplitude (A) - maximum position from the equilibrium position/the most that it is stretched out

Period -T - time to complete one cycle.

Frequency - f - number of complete cycles per unit of time

f = 1/T inverse of each other

Accelerating Springs sum of forces = ma -kx = ma a = (-k/m)x maximum position at amplitudes mass causes different elongations(x position) Force and direction are directly proportional KE1 + PEg1 + PEe1 = KE2 + PEg2 + PEe2 PEspring = (1/2)kx^2

Conservation of energy applies to spring motion - total mechanical energy of a block and spring remains constant

E = (1/2)MVo^2 spring and object not attached or object bounces off E = (1/2)mv^2 + (1/2)kx^2 compressing E = (1/2)kA^2 rest, V = 0 compressed

Velocity in SHM applying conservation of energy (1/2)kA^2 = (1/2)mv^2 + (1/2)kx^2 v = square root of (k/m)(A^2 - x^2)

Circular and Simple Harmonic Motions SHM is a projection of circular motion onto an axis

the radius of a circle is the amplitude of SHM

Circular Equations Vo = 2(pi)A/T T = 2(pi)A/(Vo) (1/2)kA^2 = (1/2)m(Vo^2) A/Vo = square root of m/k

Period os SHM (spring) T = 2(pi)(square root of m/k) T depends on mass and spring constant the less mass, the period faster if you add mass, then the slower the period

Frequency - number of oscillations(cycles) per unit of time f = 1/T unit of frequency is Hz = s^-1 = cycles/s

Angular Frequency w = 2(pi)f = square root of (k/m)

Simple Pendulum restoring force(SHM) pulled back to equilibrium

Pendulum and Spring For the period, mass does not affect it, but length and g do affect it

Damping is the reduction in Amplitude over time

Wave Motion Work - apply a force through a distance energy is hte ability to do work waves transfer energy

2 ways to transfer energy - by matter and by waves Waves form through vibrations Types of waves - longitudinal - particles of the medium vibrate parallel to the direction of the propagation A longitudinal wave can be created in a slinky if the slinky is stretched out horizontally and the end coil is vibrated back-and-forth in a horizontal direction.

A compression is a point on a medium through which a longitudinal wave is traveling which has the maximum density. A region where the coils are spread apart, thus maximizing the distance between coils, is known as a rarefaction. A rarefaction is a point on a medium through which a longitudinal wave is traveling which has the minimum density.

Transverse - particles of the medium vibrate perpendicular to the direction of propagation A transverse wave can be created in a rope if the rope is stretched out horizontally and the end is vibrated back-and-forth in a vertical direction.

Classes of waves Mechanical - requires a medium A medium is a substance or material which carries the wave. The wave medium is not the wave and it doesn't make the wave; it carries or transports the wave from its source to other locations. Electromagnetic - does not require a medium

Parts of a wave crest, amplitude, equilibrium position, wavelength, and trough The crest of a wave is the point on the medium which exhibits the maximum amount of positive or upwards displacement from the rest position The trough of a wave is the point on the medium which exhibits the maximum amount of negative or downwards displacement from the rest position. The wavelength of a wave is simply the length of one complete wave cycle.

A wave is a repeating pattern. It repeats itself in a periodic and regular fashion over both time and space. And the length of one such spatial repetition (known as a wave cycle) is the wavelength. The wavelength can be measured as the distance from crest to crest or from trough to trough. In fact, the wavelength of a wave can be measured as the distance from a point on a wave to the corresponding point on the next cycle of the wave.

Wave Speed v = x/t v = wavelength/period v = wavelength(frequency)

The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. In the case of a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. In equation form

Wave Properties waves occur from vibrations Reflection - bouncing back of waves after hit something Refraction?Transmission - when the wave goes into a different material/medium/the bending of waves ex - a wave going from deep water to shallow water ex - a wave going around a turn or bend Resonance/Standing Waves Diffraction - ability of a wave to go through or around objects Interference - 2 waves in the same spot at the same medium at the same time

Waves at boundaries Some of the waves reflect and some of the waves refract

Reflection - bouncing back of waves barrier normal incident reflected

Refraction - waves move from one medium to another. When the wave is transmitted, it changes speed. The change in speed causes it to change direction, so the refraction is also defined as the bending of waves. When the material is changed, the direction is changed, so the speed changes when transmitted

Frequency is constant to refraction, so water travels slower in shallow water

Standing Waves A wave and its reflection appear to stand still Node and Anti-Node A standing wave pattern always consists of an alternating pattern of nodes and antinodes. When a standing wave pattern is established in a medium, the nodes and the antinodes are always located at the same position along the medium; they are standing still. The nodes are produced at locations where destructive interference occurs. Anti-nodes are produced at locations where constructive interference occurs.

Interference - two or more waves occupy the same point in a medium at the same time Superposition is the calculation of the height of the new wave. The sum of the amplitudes(or displacements) at that point.

Constructive - when waves are in phase Destructive - when waves are out of phase

Diffraction - ability of a wave to go around obstacles ot through openings Longer wavelength means more diffraction Smaller opening - more it diffracts

For more information about waves, visit www.glenbrook.k12.il.us/ GBSSCI/PHYS/CLASS/waves/u10l2a.html