AP Physics B (Princeton 15 & Giancoli 11 & 12)

1. AP Physics B(Princeton 15 &Giancoli 11 & 12) Waves and Sound

2. Assignments Reading: 11.1-4,7-9,11-13 and 12.1,2,4-7 and Princeton 15 Problems: Waves: 11.42,43,55,56 Sound: 12.4,5,10,11 Strings/AirColumns12.29,30,35 Interference 12.42,43 Doppler 12.51,52 SHM: 11.4,5,20, 25 Pendulum: 11.31,32

3. Preview • What are the two categories of waves with regard to mode of travel? • Mechanical • Electromagnetic • Which type of wave requires a medium? • Mechanical • An example of a mechanical wave? • Sound

4. Velocity of a Wave • The speed of a wave is the distance traveled by a given point on the wave (such as a crest) in a given internal of time. • v = d/t d: distance (m) t: time (s) • v = f l v: speed (m/s) l: wavelength (m) f : frequency (s-1, Hz)

5. Period of a Wave T = 1/f T : Period = (s) F : frequency (s-1, Hz)

6. Problem: Sound travels at approximately 340 m/s, and light travels at 3.0 x 108 m/s. How far away is a lightning strike if the sound of the thunder arrives at a location 5.0 seconds after the lightning is seen? Light travels almost instantaneously from strike location to the observer. The sound travels much more slowly: d = vs t = (340 m/s)(5.0 s) = 170m

7. Problem: The frequency of a C key on the piano is 262 Hz. What is the period of this note? What is the wavelength? Assume speed of sound in air to be 340 m/s at 20 oC. T = 1/f = 1/262 s-1 = 0.00382 s V = f l l = v/f l = 340 m/s / 262 /s = 1.30 m

8. Problem A sound wave traveling through water has a frequency of 500 Hz and a wavelength of 3 m. How fast does sound travel through water? v = l f = 3m (500 Hz) = 1500 m/s

9. Wave on a Wire v = FT m / L v, velocity, m/s FT, tension on a wire, N m/L mass/unit length, kg/m m/L may be shown as m

10. Problem Ex. 11-11 A wave whose wavelength is 0.30 m is traveling down a 300 m long wire whose total mass is 15 kg. If the tension of the wire is 1000N, what are the speed and frequency of the wave? Using equation on prior slide: v = √[( 1000N) / (15kg)(300m)] = 140m/s f = v / l = 140 m/s / 0.30 m = 470 Hz

11. Types of Waves • A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction which the wave moves. • Example: Waves on a guitar string • A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction which the wave moves. These are also called compression waves. • Example: Sound • http://einstein.byu.edu/~masong/HTMstuff/WaveTrans.html

12. What are two types of wave shapes? Transverse Longitudinal

13. http://www.school-for-champions.com/science/sound.htm

14. Transverse Wave Type

15. Longitudinal Wave Type

16. Longitudinal vs Transverse

17. Other Waves Types Occurring in Nature Light: electromagnetic Ocean waves: surface Earthquakes: combination Wave demos: http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html http://www.kettering.edu/~drussell/Demos/doppler/mach1.html

18. Properties of Waves Reflection occurs when a wave strikes a medium boundary and “bounces back” into the original medium. Those waves completely reflected have the same energy and speed as the original wave.

19. Types of Reflection Fixed-end Reflection- The wave reflects with inverted phase. Open-end Reflection- The wave reflects with The same phase. www.iop.org/activity/education/Teaching_Resources

20. Refraction of Waves • Wave is transmitted from one medium to another. • Refracted waves may change speed and Wavelength • Almost always is accompanied by some reflection. • Refracted waves do not change frequency.

21. Sound - a longitudinal wave Sound travels through air about 340 m/s.vair=331 + 0.6T Sound travels through other media as well, often much faster than 340 m/s. Sound waves are started by vibration of some other material, which starts the air vibrating. www.silcom.com/~aludwig/musicand.htm

22. Sound – a longitudinal wave

23. Hearing Sounds http://www.allegropianoworks.com/assets/rare_compress.jpg We hear a sound as “high” or “low” pitch depending on the frequency or wavelength. High-pitched sounds have short wavelengths and high frequencies. Low-pitched sounds have long wavelengths and low frequencies. Humans hear from about 20 Hz to about 20,000 Hz. The amplitude of a sound’s vibration is interpreted as its loudness. We measure loudness (also known as sound intensity) on the decibel scale, which is logarithmic.

24. Doppler Effect The Doppler Effect is the apparent change in pitch of a sound as a result of the relative motion of an observer and the source of a sound. Coming toward you a car horn appears higher pitched because the wavelength has been effectively decreased by the motion of the car relative to you. The opposite occurs when you are behind the car. http://people.finearts.uvic.ca/~aschloss/course_mat/MU207/images/Image2.gif

25. Pure Sound • Sounds are longitudinal waves, but they can be shown to look like transverse waves. • When air motion is graphed in a pure sound tone versus position, we get what looks like a sine or cosine function. • A tuning fork produces a relatively pure tone as does a human whistle.

26. Graphing a Sound Wave

27. Complex Sounds Because of superposition and interference, real world waveforms may not appear to be pure sine or cosine functions. This is because most real world sounds are composed of multiple frequencies. The human voice and most musical instruments are examples.

28. The Oscilloscope With an Oscilloscope we can view waveforms. Pure tones will resemble sine or cosine functions, and complex tones will show other repeating patterns that are formed from multiple sine and cosine functions added together. (Amplitude vs time.)

29. The Fourier Transform The Fourier transform has long been used for characterizing linear systems and for identifying the frequency components making up a continuous waveform. This mathematical technique separates a complex waveform into its component frequencies. The Fourier Transform´s ability to represent time-domain data in the frequency domain and vice-versa has many applications. One of the most frequent applications is analysing the spectral (frequency) energy contained in data that has been sampled at evenly-spaced time intervals. Other applications include fast computation of convolution (linear systems responses, digital filtering, correlation (time-delay estimation, similarity measurements) and time-frequency analysis.

30. Fourier Transform - showing “time domain” and “frequency domain”.

31. Superposition Principle When two or more waves pass a particular point in a medium simultaneously, the resulting displacement of the medium at that point is the sum of the displacements due to each individual wave. The waves are said to interfere with each other.

32. Superposition of Waves When two or more waves meet, the displacement at any point of the medium is equal to the algebraic sum of the displacements due to the individual waves.

33. Types of Interference If the waves are in phase, when crests and troughs are aligned, the amplitude in increased and this is called constructive interference. If the waves are “out of phase”, when crests and troughs are completely misaligned, the amplitude is decreased and can even be zero. This is called destructive interference.

34. Constructive Interference Crests are Aligned  the waves are “in phase”

35. Destructive Interference Crests are aligned with troughs  Waves are “out of phase”

36. Constructive & Destructive Interference

37. Interference Problem: Draw the waveform from the two components shown below.

38. Standing Waves A standing wave is one which is reflected back and forth between fixes ends of a string or pipe. Reflection may be fixed or open-ended. Superposition of the wave upon itself results in a pattern of constructive and destructive interference and an enhanced wave. Let’s see a simulation http://www.5min.com/Video/The-Rubens-Tube-Frequency-of-Fire-1858291

39. Fixed-end standing waves - guitar or violin string http://id.mind.net/~zona/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html Fundamental 1st harmonic l = 2L First overtone 2nd harmonic l = L Second Overtone 3rd harmonic l = 2L/3

40. Problem A string of length 12 m that’s fixed at both ends supports a standing wave with a total of 5 nodes. What are the harmonic number and wavelength of this standing wave? L = 4(1/2 l )  l = 2L/4 4th harmonic since it matches ln = 2L/n for n = 4 wavelength: l4 = 2(12m) / 4 = 6 m

41. Open-ended standing waves - flute & clarinet l = 2L l = L l = (2/3)L • = 4L • l = (4/3)L • l = (4/5L

42. physics.indiana.edu/~p105_f02/standing_waves_...

43. http://upload.wikimedia.org/wikibooks/en/3/32/Fhsst_waves40.pnghttp://upload.wikimedia.org/wikibooks/en/3/32/Fhsst_waves40.png • open ends one end both ends • closed closed

44. Sample Problem 12-30. a) Determine the length of an organ pipe that emits middle C (262Hz). The air temp. is 21oC. A) v = 331m/s + 0.6 m/soC(21oC) = 344m/s A) l = 2L v = fl = 2lf L = v/2f = 344m/s/{2(262/s)] L = 0.656m B) What are the wavelength and frequency of the 1st harmonic? Frequency is 262 Hz Wavelength is twice the length of the pipe, 1.31 m. C) What is the wavelength and frequency in the traveling sound wave produced in the outside air? They are the same because it is air that is resonating in the organ pipe: 262Hz and 1.31 m

45. Superposition of 2 sound waves http://www.ece.utexas.edu/~nodog/me379m/superposition.html

46. Resonance and Beats Resonance occurs when a vibration from one oscillator occurs at a natural frequency for another oscillator. The first oscillator will cause the second to vibrate. See next slide.

47. Resonance http://www.isd-dc.org/ISD-Wash/GIFS%20Pictures%20&%20Whatnots/tuningforkresonance.jpg

48. Beats The word physicists use to describe the characteristic loud/soft pattern that characterizes two nearly matched frequencies. Musicians call this “being out of tune”.

49. Beats When two sound waves whose frequencies are close but not exactly the same, the resulting sound modulates in amplitude changing from loud to soft to loud. This is called beat frequency and is shown by: fbeat = f 1 - f 2

50. Sound Level Intensity: Rate at which sound waves transmit energy is measured in energy per unit area: watt/m2 or watt/cm 2 Intensity level or loudness level, B B = 10log I/Io where Io = 1x10-12 w/m2 or 1x10-16 w/cm2