Types of Waves (1)

1. Types of Waves (1) • Mechanical waves and electromagnetic waves Some waves require a material substance called a medium through which to travel. Waves like this are called mechanical waves. Examples: water waves, sound waves and seismic waves etc. Electromagnetic waves require no medium through which to travel. Example: radio waves, microwaves and light etc.

2. Types of Waves (2) http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html • Transverse waves and longitudinal waves In transverse wave, the direction in which the disturbances take place is at right angles to the direction of propagation of the waves. In longitudinal wave, the disturbances take place in a direction parallel to the direction of propagation of the waves. http://www.cbu.edu/~jvarrian/applets/waves1/lontra_g.htm

3. Types of Waves (3) • Progressive waves and stationary waves A wave which transmits energy from the source to the space surrounding the source is called a progressive wave (travelling waves). In certain conditions, waves energy is localized. When this happens, the waves are called stationary waves (standing waves).

4. Comparison of stationary waves and progressive waves Stationary waves Travelling waves Waveform does not move, but has nodes at fixed places, energy is not carried away. Waveform moves through the medium, carrying energy, but not the medium, with it. The amplitude varies from zero at a node to maximum at an antinode. The amplitude is the same for all particles along the wave. All the particles between two adjacent nodes are in phase. Over one wavelength all particles have different phases.

5. Wave Equations • In a sinusoidal wave, each particle undergoes simple harmonic motion about its equilibrium position.This gives the equation where  = 2 f or where k = 2π/λ

6. y A 0 T 2T t Variation of Displacement with Time • The graph shows how the displacement of one particle at a particular distance from the source varies with time. • Graph of the equation

7. y A 0 λ 2λ x Variation of displacement with distance • The graph shows the displacement of the vibrating particles at different distances from the source at a certain instant. • Graph of the equation

8. or Wave Function for a Sinusoidal wave (1) • Mathematically the variable y depends on two variables xand t. So the combined equation is

9. displacement B starts here A 0 time Phase Difference • The phase difference between two waves is the fraction of a cycle (in radians) by which one wave would have to be advanced or retarded to be in phase with the other. B is ¼ cycle behind A

10. Velocity of Propagation of Mechanical Waves (1) • It is usually found that the speed of a mechanical wave is affected by two factors. • One of the factors is associated with the strength of the elastic coupling between particles in the medium through which the waves travels. • The other factor is associated with the inertia of the moving particles.

11. Velocity of Propagation of Mechanical Waves (2) Equations giving the speed of different types of wave

12. Huygens’ Principle http://id.mind.net/~zona/mstm/physics/waves/propagation/huygens1.html • Every point on a wavefront can be considered as a source of tiny wavelets that spread out in the forward direction at a speed of the wave itself. • The new wavefronts is the envelop of all the wavelets – that is, the tangent to all of them.

13. B vt B’ vt A A’ Huygens’ Principle and the Law of Reflection • The angle of incidence=the angle of reflection http://www.walter-fendt.de/ph14e/huygenspr.htm

14. v1t v2t Huygens’Principle and the Law of Refraction • Sin i/sin r = v1/v2 = 1/2 B B’ A’ A

15. Phase Change on Reflection (1) http://surendranath.tripod.com/Applets.html • Fixed end reflection There is a phase Change of  after reflection

16. Phase Change on Reflection (2) • A wave travelling from a less dense medium to a denser medium

17. Phase Change on Reflection (3) • Free end reflection No phase change occurs

18. Phase Change on Reflection (4) • A wave travelling from a denser medium to a less dense medium

19. Fixed end Free end Phase Change on Reflection (5) • Phase changes also occurs when longitudinal waves are reflected (e.g. Sound waves). R C R C C R R C

20. Uses of Reflected Waves • Radar (Radio Detection And Ranging) • Pulses of high-frequency radio waves are transmitted towards distant objects and their reflections are received between the transmitted pulse. • Sonar (Sound Navigation And Ranging) • Pulses of ultrasonic wave are transmitted towards under water objects, and their reflected pulses are detected. • Ionospheric Waves • Radio waves from the transmitter travels through air and is reflected by the ionosphere. http://www.pbs.org/wgbh/nova/lochness/sonar2.html

21. Uses of Radar • Detect the presence of an object at a distance • Detect the speed of an object • Map something- • to create detailed topographic maps of the surface of planets and moons. http://www.howstuffworks.com/radar2.htm

22. Uses of Sonar • Depth sounders • To measure the depth of the sea • Fish finders • To detect shoals of fish • Side Scan sonar • To map the ocean floor http://www.pbs.org/wgbh/nova/lochness/sonar.html

23. Atmospheric Windows to EM Radiation

24. Reflection of Radio Waves from the Ionosphere

25. Propagation of Radio Waves

26. Superposition of waves http://www2.biglobe.ne.jp/~norimari/science/JavaEd/e-wave2.html • Principle of superposition • Pulses and waves pass through each other unaffected. • The total displacement is the vector sum of the individual displacements due to each wave.

27. Interference http://www.colorado.edu/physics/2000/schroedinger/index.html • Constructive interference • Path difference =n • Destructive interference • Path difference = (n+½)

28. Beats http://surendranath.tripod.com/Applets.html • Beats are formed when two waves with slightly different frequencies interfere with each other. http://www.school-for-champions.com/science/sound_beat.htm

29. Beat Frequencies • Beat frequency is the combination of two frequencies that are very close to each other. The sound will fluctuate in volume according to the difference in their frequencies. • fb = | f1 − f2 | where • fbis the beat frequency • f1 and f2 are the two sound frequencies • | f1 − f2 | is the absolute value or positive (+) value of the difference

30. Applications of Beats • Tuning of Musical Instruments • A piano tuner will strike a key and then compare the note with a tuning fork. If the piano is slightly out of tune, he will be able to hear the beat frequency and then adjust the piano wire until it is at the same frequency as the tuning fork. • Police RADAR • the beat frequency between the directed and reflected waves provides a measure of the vehicle speed.

31.  Transverse waves • Particles vibrate along a line which isperpendicularto the direction of travel of the disturbance.

32.  Longitudinal Waves • Particles vibrate along a line which isparallel to the direction of travel of the disturbance.

33.  Stationary Waves • A stationary wave doesn’t appear to be travelling. Nodes Antinodes

34. Useful Websites • Reflection of waves • http://www.cdli.ca/courses/phys2204/unit04_org01_ilo07/b_activity.html • http://phoenix.phys.clemson.edu/labs/224/microwaves/index.html#setup • http://www.scienceinschool.org/2009/issue12/microwaves

35. Interference of microwaves (1)

36. Interference of microwaves (2) • Procedure • Set up the transmitter symmetrically behind the two gaps, each of which is a half-wavelength wide. • Move the receiver in an arc, always the same distance from the gaps. The current through the meter should rise and fall to show about five maxima. • Show that, when either gap is covered with a metal plate, the received signal decreases if the receiver is at a maximum but increases if the receiver is at a minimum.

37. Interference of microwaves (3)