Waves, Optics, Waves, Optics, Oscillation, and Oscillation, and

GravitationGravitation

By: Charnae’ Kearney By: Charnae’ Kearney

and and Andy Hurst Andy Hurst

Traveling WaveTraveling Wave

Any kind of wave which propagates in a Any kind of wave which propagates in a single direction with negligible change in single direction with negligible change in shape.shape.

Traveling waves are observed when a Traveling waves are observed when a wave is not confined to a given space wave is not confined to a given space along the medium. The most commonly along the medium. The most commonly observed traveling wave is an ocean wave observed traveling wave is an ocean wave

Traveling and Standing WavesTraveling and Standing Waves An important class of traveling waves is plane waves in air which create An important class of traveling waves is plane waves in air which create

standing waves in rectangular enclosures such as ``shoebox'' shaped standing waves in rectangular enclosures such as ``shoebox'' shaped concert halls. concert halls.

Standing waves don't go anywhere, but they do have regions where the Standing waves don't go anywhere, but they do have regions where the disturbance of the wave is quite small, almost zero. These locations are disturbance of the wave is quite small, almost zero. These locations are called nodes. There are also regions where the disturbance is quite intense, called nodes. There are also regions where the disturbance is quite intense, greater than anywhere else in the medium, called antinodes. greater than anywhere else in the medium, called antinodes.

Standing waves don't go anywhere, but they do have regions where the Standing waves don't go anywhere, but they do have regions where the disturbance of the wave is quite small, almost zero. These locations are disturbance of the wave is quite small, almost zero. These locations are called nodes. There are also regions where the disturbance is quite intense, called nodes. There are also regions where the disturbance is quite intense, greater than anywhere else in the medium, called antinodes. greater than anywhere else in the medium, called antinodes.

Wave PropagationWave Propagation Any of the waves that waves travelAny of the waves that waves travel With respect to the direction of the oscillation relative to the propagation With respect to the direction of the oscillation relative to the propagation

direction, we can distinguish between longitudinal wave and transverse direction, we can distinguish between longitudinal wave and transverse waves.waves.

For electromagnetic waves, propagation may occur in a vacuum as well as For electromagnetic waves, propagation may occur in a vacuum as well as in a material medium. Most other wave types cannot propagate through in a material medium. Most other wave types cannot propagate through vacuum and need a transmission medium to exist.vacuum and need a transmission medium to exist.

Another useful parameter for describing the propagation is the wave Another useful parameter for describing the propagation is the wave velocity that mostly depends on some kind of density of the medium.velocity that mostly depends on some kind of density of the medium.

Principle of SuperpositionPrinciple of Superposition

The regions where they overlap, the The regions where they overlap, the resultant displacement is the algebraic resultant displacement is the algebraic sum of their separate displacements.sum of their separate displacements.

Simple Harmonic MotionSimple Harmonic Motion Regular, repeated, friction-free motion in which Regular, repeated, friction-free motion in which

the restoring force has the mathematical form the restoring force has the mathematical form F= F= -kx-kx

Common examples: mass on a spring and a Common examples: mass on a spring and a pendulumpendulum

The word “harmonic” refers to the motion being The word “harmonic” refers to the motion being sinusoidal, it is “simple” when there is pure sinusoidal, it is “simple” when there is pure sinusoidal motion of a single frequencysinusoidal motion of a single frequency

As an object vibrates in harmonic motion, energy As an object vibrates in harmonic motion, energy is transferred between potential and kinetic is transferred between potential and kinetic energy.energy.

Mass on a SpringMass on a Spring

When it vibrates it has both a period and a When it vibrates it has both a period and a frequencyfrequency

Restoring force – the force trying to Restoring force – the force trying to restore it (mass on a spring) back towards restore it (mass on a spring) back towards the center of the oscillationthe center of the oscillation

PendulumPendulum

A mass on the end of a string which A mass on the end of a string which oscillates in harmonic motionoscillates in harmonic motion

T= 2T= 2π√π√L/GL/G L is the length of the pendulum L is the length of the pendulum G is the acceleration due to gravityG is the acceleration due to gravity

Newton’s Law of GravityNewton’s Law of Gravity

Every point mass in the universe attracts Every point mass in the universe attracts every other point mass with a force that is every other point mass with a force that is directly proportional to the product of their directly proportional to the product of their masses and inversely proportional to the masses and inversely proportional to the square of the distance between them.square of the distance between them.

F= G mF= G m11 m m22

--------------------------------------------------

rr²²

                ,

F is the force between the masses, G is the gravitational constant,

m1 is the first mass, m2 is the second mass, and

r is the distance between the masses.

Newton’s Law of Gravity Contin.Newton’s Law of Gravity Contin.

Gravitation is a Gravitation is a UNIVERSALUNIVERSAL force force between all objects in the universe.between all objects in the universe.

The force on the Earth of moon was The force on the Earth of moon was identical to the force of the Earth on the identical to the force of the Earth on the apple.apple.

Circular Orbits of Planets & SatellitesCircular Orbits of Planets & Satellites As a satellite orbits the earth, it is pulled toward As a satellite orbits the earth, it is pulled toward

the earth with a gravitational force which is the earth with a gravitational force which is acting as a centripetal force. The inertia of the acting as a centripetal force. The inertia of the satellite causes it to tend to follow a straight-line satellite causes it to tend to follow a straight-line path, but the centripetal gravitational force pulls path, but the centripetal gravitational force pulls it toward the center of the orbit. it toward the center of the orbit.

If a satellite of mass If a satellite of mass mm moves in a circular orbit moves in a circular orbit around a planet of mass around a planet of mass MM, we can set the , we can set the centripetal force equal to the gravitational force centripetal force equal to the gravitational force and solve for the speed of the satellite orbiting at and solve for the speed of the satellite orbiting at a particular distance a particular distance rr::

r

GMv

r

GmM

r

mv

FF Gc

2

2

General Orbits of Planets & General Orbits of Planets & SatellitesSatellites

Elliptical Motion:Elliptical Motion:

Kepler’s Law of Planetary MotionKepler’s Law of Planetary Motion The orbit of every planet is an ellipse with the The orbit of every planet is an ellipse with the

Sun at one of the two foci. Sun at one of the two foci. A line joining a planet and the Sun sweeps out A line joining a planet and the Sun sweeps out

equal areas during equal intervals of time.equal areas during equal intervals of time.[1][1] The square of the orbital period of a planet is The square of the orbital period of a planet is

directly proportional to the cube of the semi-directly proportional to the cube of the semi-major axis of its orbit major axis of its orbit