What are waves? A wave is a transfer of energy from one place to another. Waves take many forms. Wave Characteristics include: Amplitude Wavelength Frequency Period Wave Speed

Transverse Waves particles in the medium vibrate perpendicularly to the line of wave speed Examples: water waves, waves on a string wavelength crest amplitude trough

Longitudinal Waves (Compressional Waves) particles in the medium vibrate parallel to the wave velocity made up of alternating areas of high pressure (compressions) and low pressure (rarefactions) Examples: Sound waves, slinky waves compression rarefaction

Mechanical Waves Waves that require a medium to transfer energy. May be either transverse or compressional (longitudinal). Examples: Sound waves, water waves, earthquake waves, waves in a string

Electromagnetic Waves Waves that consist of an electric field and a magnetic field working to propagate it through free space (a vacuum) No medium required Best modeled using transverse waves All EM waves travel at the speed of light, c c = 3 x 108 m/s Examples: light waves, microwaves, ultraviolet, infrared, radar, radio waves, gamma rays, x-rays, etc.

Wave Characteristics

Amplitude Amplitude - the maximum displacement of the medium measured from the rest position. Indicates the amount of energy carried by the wave Crest - highest point on waveform, maximum displacement of medium Trough - lowest point on waveform, maximum displacement of medium

Wavelength The distance between corresponding points on consecutive waves.

Frequency Frequency (f or n) - the number of complete cycles (waves) that pass a given point in the medium in 1 second. Measured in Hertz(Hz). 1 Hz = 1 cycle/sec. stays the same when the wave goes from one medium to another

Period Period (T) - the time it takes for one complete cycle to pass a given point in the medium, or the time that passes before the motion repeats itself. Measured in seconds. f = 1/T T = 1/f

v = lf or v = ln Wave Speed velocity the wave travels through a medium velocity is determined by the medium v = lf or v = ln “nu” - another symbol for frequency

Wave Behaviors

Reflection Reflection is when wave changes directions because it encounters a barrier. barrier normal Incident wave i Reflected wave r Law of Reflection: i = r “Angle of incidence = Angle of reflection”

Refraction Refraction occurs when a wave bends as is passes from one medium to another (crossing a boundary). Medium determines wave speed and when wave speed changes, the wave bends. water normal air Incident wave Boundary (water surface) Refracted wave

Diffraction The bending of waves around the edge of a barrier.

Boundaries When a wave encounters the boundary between two media some will be reflected and some will be transmitted. How much goes each way is determined by the relative densities of the media. The transmitted pulses will always be erect (right side up)

Crossing Boundaries Less Dense to More Dense When a wave is moving from a less dense medium to a more dense medium, the reflected pulse is inverted. v Before Less dense medium More dense medium v After v

Crossing Boundaries More Dense to Less Dense When a wave is moving from a more dense medium to a less dense medium, the reflected pulse is erect. v Before More dense medium Less dense medium v v After

Interference When two or more waves occupy the same space in a medium at the same time they interfere with each other. The medium’s displacement will be the vector sum of the displacements caused by the individual waves. After the waves pass each other they will return to their original forms.

Constructive Interference When two waves interfere in a manner such that the amplitude of the resultant wave is greater than the amplitude of the individual waves.

Destructive Interference When two waves interfere in a manner such that the amplitude of the resultant wave is smaller than the amplitude of the individual waves. Note: Complete cancellation does not always occur in destructive interference.

Standing Waves Caused by a wave and its reflected wave interfering in the medium Wave pattern of alternating nodes and antinodes. Nodes - areas of no displacement of the medium caused by destructive interference Antinodes - areas of maximum displacement of the medium caused by constructive interference. Note: The wavelength of a standing wave consists of 2 antinodes. 1 wavelength is shown. node Antinode