Physics of waves

1. Physics of waves Study these and the other properties of waves for the test3/11

2. Definition • A form of energy transfer between objects, or that which transmits energy - mechanical requires a medium to transmit the energy through - non-mechanical does not require a medium to transmit energy

3. Types of waves types 1: classed by medium • mechanical • electromagnetic • gravitational • matter waves

4. types 2: classed by orientation of change • transverse • synonyms • shear • examples: • light and all electromagnetic waves • musical instruments • chordophones - vibrating strings (violin, guitar, piano) • membranophones - vibrating membranes (drums, vocal chords, kazoo?) • idiophones - vibrating solid object (bells, glockenspiel, xylophone, mbira) • seismic • secondary (S) shear • animal locomotion • vertebrates (snakes, fish)

5. Parts • crest: the high, the greatest positive displacement • trough: the low part, the lowest negative displacement

6. Type 2 • longitudinal, • synonyms • pressure, compression, density • examples • sound • musical instruments • aerophones - vibrating columns of air (horns, whistles, organ pipes ) • seismic • primary (P) pressure • animal locomotion • invertebrates (worms) • traffic jams • density waves in spiral galaxies generate the arms

8. Parts • compressions (a.k.a. condensation): the pressed part, the greatest positive pressure change, a region where the medium is under compression • rarefactions (a.k.a. dilations): the stretched part, the lowest negative pressure change, a region where the medium is under tension

9. type Surface ocean wave • http://physics.info/waves/ • surface, interface, complex • ocean

10. Type 2 • seismic waves come in two basic families • body waves, which have already been discussed • Primary (longitudinal, compression, Pressure) • Secondary (transverse, Shear), can't propagate through liquids • surface waves, which are what this discussion is a part of • Love, (Lateral shear) • Rayleigh, (elliptical, plate waves, ground Roll), something like ocean waves, but elliptical instead of circular

12. Type 2 • torsional • ribbons, plates, bars • bridges, skyscrapers • unclassifiable • animals • arthropod locomotion (centipedes, millipedes, caterpillars) • peristalsis • nerve impulses • heart contractions • dominoes

13. types 3 classified by duration • episodic • periodic speed, amplitude, wavelength, period, phase, frequency seismic energy propagates through the Earth within the 50 Hz to 0.001 Hz range! The expression "long period" (greater than 10 seconds) and "short period" (less than 1 second or greater than 1 Hz)

14. types 4 classified by appearance • traveling • standing

15. Summary • Properties • A wave is a disturbance that propagates through a medium. • Propagation describes the spreading of a disturbance. • Waves transfer energy, momentum, and information, but not mass

16. Classifying waves by medium • Mechanical Waves • Matter is the medium. • Sound is a mechanical wave. • Electromagnetic Waves • Electric and magnetic fields are the media. • Light is an electromagnetic wave. • Gravitational Waves • The gravitational field is the medium. • The existence of gravitational waves has not yet been confirmed

17. Mechanical vs electromagnetic waves

18. Two-dimensional representation of gravitational waves generated by two neutron stars orbiting each other

20. Radio spectrum Commercial radio 300MHz

21. Electromagnetic wave

22. Classifying waves by orientation • Transverse Waves • The disturbance is perpendicular to the direction of propagation. • All electromagnetic waves are transverse. This includes light. • A crest is a point of maximal change in the positive direction. • A trough is a point of maximal change in the negative direction. • Longitudinal Waves • The disturbance is parallel to the direction of propagation. • Sound is a longitudinal wave. • A compression or condensation is a region where the medium is under compression. • A rarefaction or dilation is a region where the medium is under tension.

24. Classifying waves by orientation • Surface Waves or Complex Waves • A combination transverse–longitudinal wave that forms near the surface of some media. • Deep water waves are surface waves. • Torsional Waves • The disturbance causes the medium to twist

25. Classifying waves by duration • adj. episodic; noun pulse • The disturbance is momentary and sudden. • adj. periodic, harmonic; noun wave train • The disturbance repeats at regular intervals

26. Classifying waves by appearance • Traveling Waves • Appear to move. • Standing Waves • Do not appear to move

28. Characteristics of periodic waves • Amplitude (A) • The maximum absolute value of a periodically varying quantity. • Amplitude has the unit of the quantity that is changing (ex. displacement, pressure, field strength, etc.) • Period (T) • The time between successive cycles of a repeating sequence of events. • T = t/n (time per number of cycles) • The SI unit of period is the second [s].

29. Frequency (ƒ) • The number of cycles of a repeating sequence of events in a unit interval of time. • ƒ = n/t (number of cycles per time) • Frequency and period are reciprocals (or inverses) of one another: ƒ = 1/T. • The SI unit of frequency is the hertz [Hz = 1/s = s−1]. • Phase (ϕ) • The stage of development of a periodic process. • Two points on a wave with the same phase have the same… • quantity of disturbance (ex. displacement) and • rate of change of disturbance (ex. velocity). • Phase is an angular quantity. • Adjacent points in phase are separated by one complete cycle. • Adjacent points out of phase are separated by half a cycle. • The SI unit of phase is the radian, which is itself a unitless ratio [rad = m/m = Pa/Pa = (V/m)/(V/m) = etc.].

30. Wavelength (λ) • The distance between any point on a periodic wave and the next nearest point corresponding to the same portion of the wave. • Wavelength is measured between adjacent points in phase. • The SI unit of wavelength is the meter [m]. • Speed (v) • Waves propagate with a finite speed (sometimes called the wave speed) that depends upon… • the type of wave, • the composition of the medium, and • the state of the medium • v = Δs/Δt the rate of change of distance with time by definition. • v = ƒλ the product of frequency and wavelength for periodic waves. • Frequency and wavelength are inversely proportional. • Lower frequency waves have longer wavelengths. • Higher frequency waves have shorter wavelengths. • The speed of a wave is sometimes known as its wave speed. • The SI unit of speed is the meter per second [m/s].

31. One-dimensional wave equation • ◦linear version • ƒ(x, t) = A sin(2π(ft − x/λ) + ϕ) • A = amplitude • ƒ = frequency • λ = wavelength • ϕ = phase

32. ◦angular version • ƒ(x, t) = A sin(ωt − kx + ϕ) • A = amplitude • ω = angular frequency (temporal frequency), ω = 2πƒ • k = wave number (spatial frequency), k = 2π/λ • ϕ = phase

33. http://www.wsfcs.k12.nc.us/Page/5693