Topic 4 Waves

Young's Double Slit Experiment

-shined monochromatic (one wavelength) light on two narrow openings that were near each other -the light diffracted through each slit, causing circular wavefronts to spread outward -these patterns overlapped each other and created constructive (bright regions) and destructive interference (dark regions) -constructive interference maximums occur where the wave crests intersect and destructive interference minimums are in between these sections. distance between maximums = ((maximum being analyzed) (wavelength) (distance from slits to screen)) / spacing between slits distance between slits = (maximum analyzed) (wavelength) (sin(theta))

Huygen's Principle

1. Every oscillator in a wave creates spherical wavelets that propagate outward. 2. The wave front created by these oscillators is due to the combined interference of the wavelets. This occurs when waves move through narrow openings.

SHM Potential Energy

1/2m w^2 x^2

SHM Kinetic Energy

1/2mw^2 (A^2 - x^2)

Transient Oscillations

A combination of natural and forced oscillations that will eventually oscillate at the driving frequency.

Damping

A frictional force in SHM that is always in the opposite direction of motion of the oscillating particle. As the particle swings, it loses energy as it does work to overcome the resistant force. The total energy is proportional to the (amplitude)^2

Compression

A point on the wave where everything is bunched together. (High Pressure)

Rarefaction

A point where everything is far apart. (Low Pressure)

Law of Reflection

A ray (line showing the direction of light energy) must always be at right angles to the wave front. The incident angle is equal to the reflected angle. The incident ray, reflected ray, and normal all lie in the same plane.

Diffuse Reflection

A single incident light ray is scattered in all directions when light strikes a not smooth surface. Shorter wavelengths are scattered the most.

Angular Frequency

Also known as angular speed: a = -w^2 x w = sqrt(k/m)

Critical Angle

Angle of incidence where the angle of refraction is 90 degrees. Sin (angle) = n1 / n2

Node

Complete destructive interference on a standing wave; 0 amplitude

Fundamental Frequency

First harmonic; Only on standing waves

Open at both ends

Fundamental Frequency = 1/2 wavelength

String (Fundamental Frequency)

Fundamental Frequency = 1/2 wavelength

Closed at one end

Fundamental Frequency = 1/4 wavelength

Antinode

Greatest constructive interference on a standing wave; the maximum point (amplitude)

Wave Rays

Highlight the direction of the energy transfer. (Usually drawn as arrows)

Wave Fronts

Highlight the part of the wave that are moving together. For example, in water ripples the wave fronts move out in circles from the starting point. With a loudspeaker, wave fronts move out in line of half circles from the source.

Refractive Index

Less dense to more dense medium: ray refracted towards normal More dense to less dense medium: ray refracted away from normal n = sin i / sin r n = c / v n1 sin (angle1) = n2 sin (angle2)

Unpolarized Light

Light that is vibrating in more than one plane. When light is polarized in different directions, canceling each other out. For example, light from the sun. If unpolarized light passes through a polarizing filter, it will become polarized. However, only light waves oscillating in ONE direction will be able to pass through the filter.

Polarization

Light that is vibrating in one single plane. Because the oscillating electric field for light occurs in a set plane, it is polarized. Light waves can be polarized in any direction.

Traveling Waves

Light, sound, and ripples. Transfers energy from one place to another without the motion from their medium. (SHM)

Restoring Force

Must always be pointing towards the mean position and also proportional to the displacement from the mean position.

Resonance

Occurs when a system is subject to an oscillating force that is operating at exactly the same frequency as the natural frequency of the already oscillating system. Vibrations in machinery, Microwave generator, Radio receivers, Musical instruments, Greenhouse effect

Hooke's Law

Restoring Force = kx

SHM

Simple Harmonic Motion takes place when an acceleration of an object is always directed towards its displacement from a fixed point. Time period does NOT depend on amplitude.

Diffraction

The bending of a wave due to a barrier or opening. The amount of bending has to do with the size of the obstacle or opening, compared with the wavelength of the wave. Also, the reason we can hear something without having to see it.

Driving Frequency

The frequency that results from a changing force being applied to the system from the outside.

Natural Frequency

The frequency that results from a system being temporarily displaced form tits equilibrium position

Amplitude

The maximum displacement from the mean position. The measure of intensity of the oscillation.

Phase Difference

The measure of how "in step" different particles are (in radians)

Frequency

The number of oscillations completed per unit of time (the number of cycles per second)

Transverse Wave

The oscillations are at right angles to the direction of motion. Wave Top = Crest Wave Bottom = Trough Examples: Water ripples, Light, waves along a stretch rope

Longitudinal Wave

The oscillations are directed parallel to the direction of motion. Examples: Sound and Compression on a spring

Intensity

The power per unit area that is received by the observer. I = A^2

Critical Damping

The resistive force is intermediate and it will allow the particle to return to its original position in the least amount of time.

Heavy damping

The resistive force is overly large and prevents the oscillations from taking place at all.

Light damping

The resistive force is so small that only a fraction of the total energy is removed each cycle. The time period of the oscillations is not affected.

Wavelength

The shortest distance along the wave between two points that are in phase with each other. From crest to crest or compression to compression.

Wave Speed

The speed at which wave fronts pass a stationary observer. v = f(wavelength)

Period

The time taken for one complete oscillation T = 1/f T = 2pi / w T = 2pi sqrt(m/k)

Similar Opening (diffraction)

The wave fronts for a circular pattern with no shadow regions.

Single Slit Diffraction

There is minimal interference as the wave moves through the slit, creating a large central maximum with smaller maximums surrounding it. Depends on the actual widths of the slits, rather than the space between them.

Principle of Superposition

There will be resulting wave that is the combination of two waves that interfere with each other.

Electromagnetic Waves

Visible light. A varying electric and magnetic field, oscillating at right angles to each other. Same speed (3 x 10^8), but differing frequencies and wavelengths.

Undamped

When SHM has total constant energy and the change in KE = the change in PE

Reflection + Transmission

When any wave meets a boundary between two different mediums, it is partially reflected and partially transmitted. The normal is the construction line that is drawn at right angles to the surface; angles are always measures between the rays and the normal.

Color Absorption and Reflection

When light strikes a surface, some wavelengths will be absorbed and some reflected. The retina can only see the reflected light.

Refraction

When plane waves are incident at an angle on a boundary between two media, the transmitted wave will change direction. The reason for this change in direction is the change in speed of the wave. FREQUENCY does not change.

Large Opening (diffraction)

When the opening is large, compared to the wavelength, the wave moves through with little diffraction. This creates large shadow regions with no wave activity to the left or right of the opening.

Constructive Interference

When two waves are in phase with one another, the amplitudes are added. It causes sound to become louder and light to become brighter.

Destructive Interference

When two waves are out of phase by pi, they cancel out entirely. Darkness instead of brightness; quiet instead of loudness.

Dispersion

When white light enters a prism and bends due to refraction to create multiple colors (the rainbow) with different wavelengths and index's of refraction. Violet and blue have the highest index's, but shortest wavelengths.

a, v, and x SHMequations

a = -Aw^2 sin(wt) v = Aw cos(wt) x = A sin(wt)

Snell's Law

sin i / sin r is constant for a given frequency sin angle 1 / sin angle 2 = V1 / V2

Mean Position

the fixed average point that an object will come back to after swinging two and fro in SHM

Displacement

the instantaneous distance of an object from its mean position