Waves
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 motion of the wave Examples: –water waves –waves on a string amplitude wavelength crest trough
Longitudinal Waves (Compressional Waves) particles in the medium vibrate parallel to the wave velocity made up of alternating areas of high density or pressure (compressions) and low density or pressure (rarefactions) Examples: Sound waves, slinky waves compressionrarefaction
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 10 8 m/s Electromagnetic waves –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 or equilibrium position. Depends on 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 (crest to crest, compression to compression, etc). Depends on frequency (inversely related) in a given medium or on speed if changing mediums.
Frequency Frequency (f - the number of complete cycles (or waves) that pass a given point in the medium per time (usually 1 sec). 1 Hertz (Hz) = 1 cycle (wave) / sec. Stays the same even when the wave goes into a different medium. Depends only on the rate (or frequency) of the source that is making the waves.
Period Period (T) - the time it takes for one complete cycle (or wave) to pass a given point in the medium, or the time that passes before the motion repeats itself. Measured in seconds. Note: frequency and period are inverses: f = 1 / T or T = 1 / f
Wave Speed Velocity or speed with which the wave travels through a medium, v Depends only on the medium. v = f or v =
Wave Behaviors
Reflection Reflection is when a wave changes directions because it encounters a barrier. rr barrier Normal Incident wave ii Reflected wave Law of Reflection: i = r “Angle of incidence = Angle of reflection”
Refraction Refraction occurs when a wave bends as it passes from one medium to another (crosses a boundary) at an angle. The wave bends because of the change in speed when it enters a different medium. Refracted ray water normal air Incident ray Boundary
Diffraction The bending of waves around the edge of a barrier or through an opening.
Boundaries When a wave encounters the boundary between two media, some of the wave 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). Both the transmitted and the reflected pulses will have a lower amplitude than the original pulse since the energy is split among them.
Crossing Boundaries Less Dense to More Dense When a wave is moving from a less dense medium to a more dense medium, the transmitted wave slows down and the reflected wave is inverted and keeps the same speed. Before v After v (same) v (less) Less dense medium More dense medium Transmitted wave - f is the same, A is less, v is less, and λ is less. Reflected wave is inverted. f, v, λ are the same and A is less.
Crossing Boundaries More Dense to Less Dense When a wave is moving from a more dense medium to a less dense medium, the transmitted wave speeds up and the reflected wave is erect and keeps the same speed. Before After Less dense medium More dense medium v v -same v - more Transmitted wave - f is the same, A is less, v is more, and λ is more. Reflected wave is erect. f, v, λ are the same and A is less.
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 at that time will be the vector sum of the displacements caused by the individual waves (crest +, trough -). After the waves pass through each other, they will look the same as they did before they met.
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 the interference of two identical waves travelling in opposite directions in a medium or by a wave and its reflected wave. 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. Node Antinode Note: One wavelength is equal to twice the distance between nodes. λ= 2 d n or d n = λ / 2 λ dndn