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# Physics 20: Waves Cheat Sheet by dianadavis

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

### 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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