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Physics 20: Waves Cheat Sheet by

Alberta Physics 20 Unit 8 Waves

Formulas

l = vΔt
Where l is the pulse length, v is the speed, and Δt is the time to create a complete pulse
v = f λ
Where v is the speed, f is the frequency in Hertz, and λ is the wavelength
L = (1/2) λ
Where L is the length of each node and λ is the wavelength
Bold formulae are not given on the Physics 20 formula sheet

Defini­tions

Wave
Travelling distur­bance that carries energy
Electromagnetic Waves
Do not require a medium to travel (light)
Mechanical Waves
Require a medium to travel (air, water, string, etc.)
Transverse Waves
The particles in the medium vibrate (or are displaced) perpen­dicular to the direction of motion of the wave
Longit­udinal Waves
The particles in the medium vibrate parallel to the direction of motion of the wave
Constr­uctive
Interf­erence
When waves in the same phase overlap, their amplitudes add together
Destru­ctive
Interf­erence
When waves of different phases overlap, their amplitudes cancel
Nodes
Points of complete destru­ctive interf­erence
Antinodes
Points of complete constr­uctive interf­erence, largest amplitude

Transverse Waves

Along the pulse, energy is stored in both elastic potential and kinetic energy
- At max displa­cement, PE is at max and KE is zero
- At equili­brium, KE is at max

The greater the amplitude, the greater the energy of the wave

Longit­udinal Waves

Examples of Wave Types

Wave Type
Exam­ple
Origin
Medium
Water Wave
Wake of boat
Boat moving
Water
Sound Wave
Stereo
Speaker vibrates
Air
Mechanical Wave
Bull whip
Arm whips
Leather
Seismic Wave
Earthquake
Shifting rock layers
Rock
Shock Wave
Atomic explosion
Nuclear fission
Air
Light Wave
Room light
Hot filament
None

Wave Behaviour

Refl­ect­ion: When a wave reflects, it exhibits a phase change (crest -> trough or vice-v­ersa)
Refr­act­ion:
Diff­rac­tion:
Inte­rfe­ren­ce:
 

Standing Waves, Nodes & Antinodes

Standing Waves: when 2 wave trains with the same amplitude and wavelength move through each other, the resulting interf­ering pattern results in a standing wave, it appears to be standing still in a constance position
- The freque­ncies at which standing waves exist are the natural or fundam­ental resonant frequency

Nodes: points of complete destru­ctive interf­erence
Anti­nod­es: points of complete constr­uctive interf­erence

Wave Behavi­ours: Reflection

Refl­ect­ion: straight waves "­bou­nce­" off a surface such that the outgoing angle (angle of reflec­tion) or reflection wave equal the incoming angle (angle of incidence) or incident wave

Angles are measure from the normal line (line perpen­dicular to the surface)

Wave Train: a series of waves linked together in phase (moving with identical motion)

Wave fronts are reflected by a barrier

Wave Behavi­ours: Refraction

When a wave passes from one medium to another through a boundary, the waves bends and changes direction (and speed) at the interface

If the medium on the other side is 'thicker' (n), then the wave will slow down and bend towards the normal line

Wave Behavi­ours: Diffra­ction

Diff­rac­tion: waves bend around a corner or opening

The amount of diffra­ction depends on the wavelength and the size of the opening

Waves lose amplitude, not speed or frequency

Wave Behavi­ours: Interf­erence

Cons­tru­cti­ve: "in phase" waves produce larger amplitudes
Dest­ruc­tive: "out of phase" waves amplitudes cancel

Prin­ciple of Superp­osi­tion: the two waves "­sup­eri­mpo­se" and "­int­erf­ere­" with each other, creating a temporary waveform that is the sum of the two waves
 

Doppler Effect

Fo = observers frequency
Fs = emitted frequency
V = speed of sound
Vs = speed of object emitting sound

Subtract when the source is moving towards the observer
Add when the source is moving away from the observer

Doppler Effect Cont.

When the source is moving towards the observer with a velocity, the waves spread out in circles around the source, the frequency doesn't change but the waves crowd together, making the wavelength shorter.

When the source is moving away from the observer, the wavelength is lengthened and the detected frequency is lower

Stringed Resonator

Stringed Resona­tor: a resonating instrument that is fixed at both ends

Closed­-Pipe Resonator

Clos­ed-Pipe Resona­tor: tube is closed at one end and open at another

In a closed­-tube, node at closed end and either node or antinode at open end.
IF antinode occurs at the open end, resonance occurs and the sound is amplified (louder).
IF a node occurs at the open end, resonance does not occur and almost no sound (hence only odd harmonics)

Open-Pipe Resonator

Open­-Pipe Resona­tor: both ends of the tube are open

Musical Instru­ments & Resonance

Fund­ame­nta­l/1st Harmon­ic: the lowest frequency making up the sound
- Wave of freque­ncies that are whole number multiples of the fundam­ental are called harmonics (2nd, 3rd, 4th, etc)
               
 

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