Waves

1. Waves

2. Types of Waves • Compression wave oscillations are in the direction of motion • Transverse Wave oscillations are transverse to the direction of motion

3. Physical Examples • Compression wave • sound waves • earthquake P-waves • Transverse Wave • water waves • earthquake S-waves • light waves

4. Wave Parameters Wavelength (l) length or size of one oscillation Amplitude (A) strength of disturbance (intensity) Frequency (f) repetition

5. Wave Properties Waves are oscillations and they transport energy. The energy of a wave is proportional to its frequency. Fast oscillation = high frequency = high energy Slow oscillation = low frequency = low energy The amplitude is a measure of the wave intensity. SOUND: amplitude corresponds to loudness LIGHT: amplitude corresponds to brightness

6. What is the Wave length? • Measure from any identical two successive points 5 10 15 20 25 30 35 40

7. What is the Wave length? • Measure from any identical two successive points 5 10 15 20 25 30 35 40 30 - 10 = 20

8. What is the Wave length? • Measure from any identical two successive points • There are 4 complete oscillations depicted here • ONE WAVE = 1 COMPLETE OSCILLATION 5 10 15 20 25 30 35 40 22.5 - 2.5 = 20

9. Frequency • Frequency = number of WAVES passing a stationary point per second (Hertz)

10. Frequency and Period Frequency (f) = number of oscillations passing by per second Period (T) = length of time for one oscillation T = 1/ff = 1/T If a source is oscillating with a period of 0.1 seconds, what is the frequency? f = 1/(0.1) = 10 Hz It will complete 10 oscillations in one second. (10 Hz) If a source oscillates every 5 seconds, its period is 5 seconds, and then the frequency is f = 1/5 = 0.2 Hz.

11. Wave Speed Wave speed depends on the wavelength and frequency. wave speed v = l f Which animal can hear a shorter wavelength? Cats (70,000 Hertz) or Bats (120,000 Hertz) l = v/f

12. Wave Speed v = l f Which animal can hear a shorter wavelength? Cats (70,000 Hertz) or Bats (120,000 Hertz) l = v/f Higher frequency = shorter wavelength Lower frequency = longer wavelength

13. Sonic Boom v > vsound

14. Doppler Effect • Change in frequency of a wave due to relative motion between source and observer. • A sound wave frequency change is noticed as a change in pitch.

15. Radial Velocity Convention True Velocity Radial = Line of Sight Component Observer Radial Velocity > 0 Moving Away No Doppler Shift Transverse motion Radial Velocity < 0 Moving Toward

16. Doppler Effect • Light

17. Line of Sight Only sensitive to motion between source and observer ALONG the line of sight.

18. Doppler Effect for Light Waves • Change in frequency of a wave due to relative motion between source and observer. • c = l f speed of light = wavelength x frequency c = 3 x 108 m/s E = hf = hc/l energy of a light wave, a photon of frequency (f) or wavelength (l) h = planck’s constant 6.63 x 10-34 J-sec A light wave change in frequency is noticed as a change in “color”.

19. Wavelength Doppler Shift l0 = at rest (laboratory) wavelength l= measured (observed) wavelength Dl= l - l0 = difference between measured and laboratory wavelength vr/c = Dl/l0 vr = (Dl/l0)c radial velocity

20. Two Equal Waves • Upon arriving in the same place, they add constructively

21. Constructive Interference • Waves combine without any phase difference • When they oscillate together (“in phase”)

22. Wave Addition Amplitude ~ Intensity

23. Two Opposite Waves • Upon arriving in the same place, they cancel, destructively

24. Destructive Interference • Waves combine differing by multiples of 1/2 wavelength • They oscillate “out-of-phase”

25. Wave Subtraction

26. Interference Computer Simulation • Water waves from two oscillating sources Ripple Tank

27. Two Slit Interference

28. Two Slit Constructive Interference • Path Length Difference = multiples of the wavelength l

29. Two Slit Destructive Interference • Path Length Difference = multiples of 1/2 l

30. Two Slit Interference • Slits are closer together, path length differences change

31. Light or Dark? • Light of wavelength 500 nm is incident in phase on the slits, is a bright or dark area observed at A-E?

32. Light or Dark? • Path Length Differences = l, Waves arrive in phase • Path Length Differences = 1/2 l, Waves arrive out of phase

33. Light or Dark? Light from the slits arrives at A. Path Length from slit 1 is 10,300 nm and from slit 2 is 10,300 nm for a difference of 0 nm. There is no path length difference so the waves from the two slits arrive at A oscillating in phase. They add constructively and produce a brighter area.

34. Light or Dark? Light from the slits arrives at E. Path Length from slit 1 is 10,800 nm and from slit 2 is 11,800 nm for a difference of 1000 nm. This path length difference is exactly two wavelengths so the waves from the two slits arrive at E oscillating in phase. They add constructively and produce a brighter area.

35. Light or Dark? Light from the slits arrives at B. Path Length from slit 1 is 10,450 nm and from slit 2 is 10,200 nm for a difference of 250 nm. This path length difference is exactly 1/2 a wavelength so the waves from the two slits arrive at B oscillating out of phase. They add destructively and produce a dark area.

36. Wave Properties Amplitude: Size of wave (perpendicular to direction of propagation) Proportional to Intensity(Sound loudness, Light brightness) Wavelength: l Size of wave (in the direction of propagation) Frequency: Number of waves passing a fixed position per second f (cycles/second, Hertz) Wave Speed: v = l f Frequency increasesFrequency decreases Energy increasesEnergy decreases Wavelength decreasesWavelength increases

37. Interactive Demonstrations On The WEB • Wave Addition • Two-slit Light Interference • Doppler Shift • Simple Geometric Optics http://pls.atu.edu/physci/physics/people/robertson/applets/applets.html

38. Dr. RobertsonPHSC 1013: Physical Science • Return to Physical Science