1. Waves

2. Definitions of Waves A wave is a traveling that carries through space and matter without transferring. Transverse Wave: A wave in which the disturbance occurs to the direction of travel. A type of transverse wave is Longitudinal Wave: A wave in which the disturbance occurs to the direction of travel of the wave. A type of longitudinal wave is Surface Wave: A wave that has charact- eristics of both and waves.

3. Types of Waves Mechanical Waves: Require a such as,, of a spring or the fabric of a rope. Electromagnetic Waves: can travel in the absence of a medium.

4. Transverse Wave Characteristics Crest:. Trough:. Amplitude: (undisturbed position). John Wiley & Sons

5. Transverse Wave Characteristics (cont.) Frequency(f): The number of the wave makes in The unit for frequency is Wavelength(): The minimum at which the wave repeats the same pattern A single oscillation is also called a The units for wavelength are

6. Transverse Wave Characteristics (cont.) Velocity (v): of the wave Measured in The formula to calculate the speed of a wave is Period (T): it takes for the wave to complete one The units for period is The formula to calculate the period is

7. Transverse vs. Longitudinal Waves

8. The Relationships v = f The of a wave is determined by the in which it travels. That means that for a given medium and are inversely proportional. As one, the other Wavelength Frequency

9. The Inverse Relationships T = As the period, the. Period Frequency

10. Speed of a Wave on a String For a stretched rope or string: Where: = Tension = linear density = As the tension, the speed. As the mass, the speed. This phenomena is commonly seen in v =

11. Waves at Boundaries A wave incident upon a fixed boundary will have its reflected back in the opposite direction. Note that the wave pulse is after reflecting off the boundary. www.electron4.phys.utk.edu

12. Interference occurs whenever two waves occupy the same space at the same time. Law of : When two or more waves are present at the same time at the same place, the disturbance is equal to the of the disturbances from the individual waves.

13. Wave Interference www.electron4.phys.utk.edu Interference – Process by which two waves meet producing a net amplitude.

14. Wave Interference Interference – Process by which two waves meet out each other.

15. Waves Wave: An interference pattern resulting from two waves moving in directions with the same and such that they develop a consistent repeating pattern of and interference.

16. Waves Node: The part of a standing wave where interference is at all times ( o out of phase). Antinode: The part of the wave where interference is maximized ().

17. Waves When a wave impacts a boundary, some of the energy is, while some passes, or may be. The wave that passes through is called a wave. A wave that is transmitted through a boundary will lose some of its energy. Electromagnetic radiation will both down and have a wavelength when going into a denser media. Sound will when transitioning into a denser media.

18. Incident + Reflected Wave Higher speed Longer wavelength Lower speed Shorter wavelength Transmitted Wave Continuous Waves – Higher Speed to Lower Speed Note the differences in wavelength and amplitude between of the wave in the two different mediums Displacement Boundary v1v1 v2v2 -v 1 Note: This phenomena is seen with light traveling from air to water.

19. The Wave Equation waves can be represented by the following equation. y(x,t) = y m sin(t - x) Where: y m =  = (2/ ) x =  = (2f) t = Note that the sum ( t - x) is in, not degrees.

20. +x The Wave Equation y(x,t) = y m sin(t -  x)  = 2/ Waveform repeats itself every.  = 2f Waveform travels through 1 (T) every. A phase constant () can be included in the phase that represents all waves that do not pass through the origin.

21. The Wave Equation – An Alternate Representation y(x,t) = y m sin(t -  x) Substituting for  (2f),  (2/) and y m (A) yields: y(x,t) = Asin2(ft - x) or y(x,t) = Asin2(vt - x) 1

22. Key Ideas Waves transfer without transferring. Longitudinal waves like that of sound require a. Transverse waves such as electro-magnetic radiation (light) do not require a. In transverse waves, displacement is to the direction of the wave while in longitudinal waves, the displacement is.

23. Key Ideas Waves can with one another resulting in or interference. waves are a special case of constructive and destructive interference for two waves moving in opposite directions with the same, and.