Waves

1. Waves Topic 4.4 Wave characteristics

2. What is a Wave? • A wave is a means by which energy is transferred between two points in a medium without any net transfer of the medium itself.

3. The Medium • The substance or object in which the wave is travelling. • When a wave travels in a medium parts of the medium do not end up at different places • The energy of the source of the wave is carried to different parts of the medium by the wave.

4. Travelling Waves • There are two types of wave motion that we encounter in the physical world. • Transverse • Longitudinal

5. Transverse • The source that produces the wave oscillates at right angles to the direction of travel of the wave • Thus, the particles of the medium through which the wave travels also oscillates at right angle to the direction of travel of the wave.

6. Transverse Wave Direction of oscillation of the particles Direction of travel of the wave

7. Longitudinal • The source that produces the wave oscillates in the same direction as the direction of travel of the wave • Thus, the particle of the medium through which the wave travels also oscillates in the same direction as the direction of travel of the wave.

8. Longitudinal Wave Direction of oscillations of the particles Direction of travel of the wave

9. Discrete Pulses and Continuous Waves • A single shake of a slinky will send a discrete pulse down it • Shake the slinky up and down and a continuous wave travels down it • This applies to longitudinal waves too

10. Wavefronts vs. Rays • All the points of disturbance that originate from a source at the same time make up the wavefront • If the source was a single point, wavefronts will be circular • If the source is a straight line, the wavefronts will be parallel • Rays are used to represent the direction of energy transfer

11. Wavefronts and rays rays Wavefronts The wavefronts typically show where the crests of the waves are. The rays are always at 90 deg to the wavefronts.

13. Displacement • (s) is the distance that any particle is away from its equilibrium position at an instance

14. Amplitude • The maximum displacement of a particle from its equilibrium position • Also equal to the maximum displacement of the source that produces the wave).

15. Wavelength • () This is the distance along the medium between two successive particles that have the same displacement and the same phase of motion. • Also, the distance traveled by the wave energy in one period

16. Period • (T) This is the time that it takes a particle to make one complete oscillation • Also equals the time for the source of the wave to make one complete oscillation. • Also equals the time for the wave energy to travel a distance equal to the wavelength of the wave

17. Frequency • (f) This is the number of oscillations made per second by a particle • Also equal to the number of oscillations made per second by the source of the wave • The SI unit of frequency is the hertz -Hz. (1 Hz is 1 oscillation per second) • Clearly then, f = 1/T

18. Wave Speed • (v, c) This is the speed with which energy is carried in the medium by the wave. • Wave speed depends only on the nature and properties of the medium

19. Intensity • Since waves transfer energy, the rate of this transfer is described by power. • The amount of power per unit area is the intensity • Intensity diminishes further from a source as the wavefronts spread out • I A2 ᴕ

20. Crest • This is a term coined from water waves and refers to the points at the maximum height of the wave.

21. Trough • A term coined from water waves referring to the points at the lowest part of the wave.

22. Wavelength again! • Wavelength will therefore be equal to the distance between successive crests and successive troughs.

23. Transverse waves Crests Troughs

24. Compression • This is a term used in connection with longitudinal wave and refers to the region where the particles of the medium are "bunched up". • High density • High pressure

25. Rarefaction • A term used in connection with longitudinal waves referring to the regions where the particles are "stretched out". • Low density • Low pressure

26. Wavelength Again!!! • The wavelength will be equal to the distance between successive points of maximum compression and successive points of maximum rarefaction.

27. Longitudinal waves Compressions and rarefactions

28. Sound Waves • A longitudinal wave in a slinky spring is analogous to a sound wave in which each turn of the spring represents an air molecule.

29. Deriving v = f  • Imagine a wave with velocity v • Being produced from a source of frequency f • In 1 second the 1st wavefront would have travelled a distance of f  • As speed = distance / time • v = f  / 1 •  v = f 

30. 2 Important Points • 1. The frequency of a wave depends only on the source producing the wave • It will therefore not change if the wave enters a different medium or the properties of the medium change

31. 2. The Speed of waves only depends on the nature and the properties of the medium • Water waves do travel faster in deeper water • Light travels slower in more optically dense material

32. Interpreting Graphs of wave motion Two types: Displacement vs. Distance Displacement vs. Time

33. Displacement / Distance displacement distance • Waves are periodic both in time and space. If we were to “freeze” time… • The y-axis shows the displacement of the wave medium from its equilibrium position • The x-axis represents the distance the wave energy has traveled from some reference point, the location of the source, typically.

34. Displacement / Distance displacement amplitude wavelength wavelength distance amplitude Note: there is no period information here!

35. Displacement / Distance displacement distance Now lets consider a single position on the wave labeled P… P If we were to “unfreeze” time and analyze how the displacement of P varies in time, the resulting diagram would look like…

36. Displacement / Time displacement time • The y-axis represents the displacement of point P from equillibrium • The x-axis represents the passage of time

37. Displacement / Time displacement amplitude period period time Note: there is no wavelength information here