Waves and Sound. An Introduction to Waves and Wave Properties Wednesday, November 19, 2008

Transcription

1 Waves and Sound An Introduction to Waves and Wave Properties Wednesday, November 19, 2008

2 Mechanical Wave A mechanical wave is a disturbance which propagates through a medium with little or no net displacement of the particles of the medium. Water Waves Wave Pulse People Wave Animation courtesy of Dr. Dan Russell, Kettering University

3 Parts of a Wave 3 crest λ: wavelength equilibrium A: amplitude -3 y(m) x(m) trough

4 Speed 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 interval of time. v = d/t d: distance (m) t: time (s) v = λƒ v : speed (m /s) λ : wavelength (m) ƒ : frequency (s 1, Hz)

5 Period of a wave T T = 1/ƒ T : period (s) ƒ : frequency (s - 1, Hz)

6 Problem: Sound travels at approximately 340 m/s,, and light travels at 3.0 x 10 8 m/s.. How far away is a lightning strike if the sound of the thunder arrives at a location 2.0 seconds after the lightning is seen?

7 Problem: The frequency of an oboe s s A is 440 Hz. What is the period of this note? What is the wavelength? Assume a speed of sound in air of 340 m/s.

8 Types of Waves Refraction and Reflection Thursday, November 20, 2008

9 Announcements Pass Post Test toward the back of the room. Calendar adjustments CPS

10 Wave Types 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 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

11 Wave types: transverse

12 Wave types: longitudinal

13 Longitudinal vs Transverse

14 Other Wave Types Earthquakes: combination Ocean waves: surface Light: electromagnetic

15 Reflection of waves Occurs when a wave strikes a medium boundary and bounces back into original medium. Completely reflected waves have the same energy and speed as original wave.

16 Reflection Types Fixed-end end reflection: The wave reflects with inverted phase. Open-end end reflection: The wave reflects with the same phase Animation courtesy of Dr. Dan Russell, Kettering University

17 Refraction of waves Transmission of wave from one medium to another. Refracted waves may change speed and wavelength. Refraction is almost always accompanied by some reflection. Refracted waves do not change frequency. Animation courtesy of Dr. Dan Russell, Kettering University

18 Sound is a longitudinal wave Sound travels through the air at approximately 340 m/s. It travels through other media as well, often much faster than that! Sound waves are started by vibration of some other material, which starts the air moving. Animation courtesy of Dr. Dan Russell, Kettering University

19 Hearing Sounds We hear a sound as high or low depending on its frequency or wavelength. Sounds with short wavelengths and high frequencies sound high-pitched to our ears, and sounds with long wavelengths and low frequencies sound low-pitched. The range of human hearing is from about 20 Hz to about 20,000 Hz. The amplitude of a sound s s vibration is interpreted as its loudness. We measure the loudness (also called sound intensity) on the decibel scale, which is logarithmic. Tom Henderson,

20 The Doppler Effect is the raising or lowering of the perceived pitch of a sound based on the relative motion of observer and source of the sound. When a car blowing its horn races toward you, the sound of its horn appears higher in pitch, since the wavelength has been effectively shortened by the motion of the car relative to you. The opposite happens when the car races away. Doppler Effect

21 Doppler Effect Stationary source Moving source Animations courtesy of Dr. Dan Russell, Kettering University Supersonic source

22 Wave Demo Day November 21, 2008

23 Superposition of Waves November 24, 2008

24 Announcement Pass in problems 2,3,5 Exam repair will be held the week after Thanksgiving during your lab period. No lunch lab this week due to Thanksgiving holiday.

25 Pure Sounds Sounds are longitudinal waves, but if we graph them right, we can make them look like transverse waves. When we graph the air motion involved 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. So does a human whistle. Later in the period, we will sample various pure sounds and see what they look like.

26 Graphing a Sound Wave

27 Complex Sounds Because of the phenomena of superposition and interference real world waveforms may not appear to be pure sine or cosine functions. That is because most real world sounds are composed of multiple frequencies. The human voice and most musical instruments produce complex sounds. Later in the period, we will sample complex sounds.

28 The Oscilloscope With the Oscilloscope we can view waveforms in the time domain.. 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.

29 The Fourier Transform We will also view waveforms in the frequency domain.. A mathematical technique called the Fourier Transform will separate a complex waveform into its component frequencies.

30 Superposition of Waves November 24, 2008

31 Announcements Pass in HW problems #2,3,5

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

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

34 Constructive Interference crests aligned with crest waves are in phase

35 Constructive Interference

36 Destructive Interference crests aligned with troughs waves are out of phase

37 Destructive Interference

38 Sample Problem: Draw the waveform from its two components.

39 Sample Problem: Draw the waveform from its two components.

40 Standing Waves November 25, 2008

41 Announcements Pass in HW problems #19,22,23 Tomorrow, you are upstairs

42 Standing Wave A standing wave is a wave which is reflected back and forth between fixed ends (of a string or pipe, for example). Reflection may be fixed or open-ended. ended. Superposition of the wave upon itself results in a pattern of constructive and destructive interference and an enhanced wave. Let s s see a simulation.

43 Fixed-end end standing waves (violin string) 1 st harmonic 2 nd harmonic Animation available at: 3 rd harmonic

44 Fixed-end end standing waves (violin string) L Fundamental First harmonic λ = 2L First Overtone Second harmonic λ = L Second Overtone Third harmonic λ = 2L/3

45 Open-end end standing waves (organ pipes) L Fundamental First harmonic λ = 2L First Overtone Second harmonic λ = L Second Overtone Third harmonic λ = 2L/3

46 Mixed standing waves (some organ pipes) L First harmonic λ = 4L Second harmonic λ = (4/3)L Third harmonic λ = (4/5)L

47 Sample Problem How long do you need to make an organ pipe that produces a fundamental frequency of middle C (256 Hz)? The speed of the sound in air is 340 m/s. A) Draw the standing wave for the first harmonic B) Calculate the pipe length. C) What is the wavelength and frequency of the 2 nd harmonic? Draw the standing wave

48 Resonance and Beats November 26, 2008

49 Announcements Pass in homework Ch 14: 47,49,51 Tonight s s HW P: 56, 60 PLUS page 8 in packet. No homework will be collected upon our return next Monday, but two assignments will be collected/checked on Tuesday.

50 Sample Problem How long do you need to make an organ pipe whose fundamental frequency is a middle C (256 Hz)? The pipe is closed on one end, and the speed of sound in air is 340 m/s. A) Draw the situation. B) Calculate the pipe length. C) What is the wavelength and frequency of the 2 nd harmonic?

51 Resonance 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. Demonstration.

52 Beats Beats is the word physicists use to describe the characteristic loud-soft pattern that characterizes two nearly (but not exactly) matched frequencies. Musicians call this being out of tune. Let s s hear (and see) a demo of this phenomenon.

53 What word best describes this to physicists? Amplitude Answer: beats

54 What word best describes this to musicians? Amplitude Answer: bad intonation (being out of tune)

55 Diffraction Monday, December 1, 2008

56 Announcements Homework will not be collected today. Tomorrow We meet downstairs. We check page 8 in your packets. We collect #59, #60 (on one page) and #66,67,69 on another. Exam repair will be done during your lunch lab period this week. Study MC on-line for MC repair; study corresponding packet FR for FR repair. Tomorrow downstairs in laboratories.

57 Diffraction Diffraction is defined as the bending of a wave around a barrier. Diffraction of waves combined with interference of the diffracted waves causes diffraction patterns. Let s s look at the diffraction phenomenon using a ripple tank.

58 Double-slit or multi-slit diffraction n=2 n=1 θ n=0 n=1

59 nλ = d sinθ Double slit diffraction n: bright band number (n = 0 for central) λ: : wavelength (m) d: space between slits (m) θ: : angle defined by central band, slit, and band n This also works for diffraction gratings consisting of many, many slits that allow the light to pass through. Each slit acts as a separate light source.

60 nλ = s sinθ Single slit diffraction n: dark band number λ: : wavelength (m) s: slit width (m) θ: : angle defined by central band, slit, and dark band

61 Sample Problem Light of wavelength 360 nm is passed through a diffraction grating that has 10,000 slits per cm. If the screen is 2.0 m from the grating, how far from the central bright band is the first order o bright band?

62 Sample Problem Light of wavelength 560 nm is passed through two slits. It is found that, on a screen 1.0 m from the slits, a bright spot is formed at x = 0, and another is formed at x = 0.03 m? What is the spacing between the slits?

63 Sample Problem Light is passed through a single slit of width 2.1 x 10-6 m. How far from the central bright band do the first and second order dark bands appear if the screen is 3.0 meters away from the slit?

64 Diffraction #2 Demos and Problems December 2, 2008

65 Periodic Motion December 3, 2008

66 Announcements Turn in problems from chapter 28, #34, 35, 54 Remember exam repair sessions during lab period

67 Periodic Motion Motion that repeats itself over a fixed and reproducible period of time is called periodic motion. The revolution of a planet about its sun is an example of periodic motion. The highly reproducible period (T) of a planet is also called its year. Mechanical devices on earth can be designed to have periodic motion. These devices are useful timers. They are called oscillators.

68 Oscillator Demo Let s see demo of an oscillating spring using DataStudio and a motion sensor.

69 Simple Harmonic Motion You attach a weight to a spring, stretch the spring past its equilibrium point and release it. The weight bobs up and down with a reproducible period, T. Plot position vs time to get a graph that resembles a sine or cosine function. The graph is sinusoidal, so the motion is referred to as simple harmonic motion. Springs and pendulums undergo simple harmonic motion and are referred to as simple harmonic oscillators.

70 Analysis of graph Equilibrium is where kinetic energy is maximum and potential energy is zero. 3 equilibrium t(s) -3 x(m)

71 Analysis of graph Maximum and minimum positions 3-3 x(m) t(s) Maximum and minimum positions have maximum potential energy and zero kinetic energy.

72 Oscillator Definitions Amplitude Maximum displacement from equilibrium. Related to energy. Period Length of time required for one oscillation. Frequency How fast the oscillator is oscillating. f = 1/T Unit: Hz or s -1

73 Sample Problem Determine the amplitude, period, and frequency of an oscillating spring using DataStudio and the motion sensors. See how this varies with the force constant of the spring and the mass attached to the spring.

74 Thursday, December 4, 2008 Friday, December 5, 2008 Springs and Pendulums

75 Announcements On Thursday, December 4 Check Packet, page 9 Collect HW, Chapter 28, pages 34,35,54 On Friday, December 5 Collect HW, Chapter 13, problems 4,5,7

76 Springs Springs are a common type of simple harmonic oscillator. Our springs are ideal springs, which means They are massless. They are both compressible and extensible. They will follow Hooke s Law. F = -kx

77 Review of Hooke s Law F s = -kx m F s mg The force constant of a spring can be determined by attaching a weight and seeing how far it stretches.

78 Period of a spring T = 2 π m k T: period (s) m: mass (kg) k: force constant (N/m)

79 Sample Problem Calculate the period of a 300-g mass attached to an ideal spring with a force constant of 25 N/m.

80 Sample Problem A 300-g mass attached to a spring undergoes simple harmonic motion with a frequency of 25 Hz. What is the force constant of the spring?

81 Sample Problem An 80-g mass attached to a spring hung vertically causes it to stretch 30 cm from its unstretched position. If the mass is set into oscillation on the end of the spring, what will be the period?

82 Spring combinations Parallel combination: springs work together. Series combination: springs work independently

83 Question? Does this combination act as parallel or series?

84 Clicker Sample Problem You wish to double the force constant of a spring. You A. Double its length by connecting it to another one just like it. B. Cut it in half. C. Add twice as much mass. D. Take half of the mass off.

85 Conservation of Energy Springs and pendulums obey conservation of energy. The equilibrium position has high kinetic energy and low potential energy. The positions of maximum displacement have high potential energy and low kinetic energy. Total energy of the oscillating system is constant.

86 Sample problem. A spring of force constant k = 200 N/m is attached to a 700-g mass oscillating between x = 1.2 and x = 2.4 meters. Where is the mass moving fastest, and how fast is it moving at that location?

87 Sample problem. A spring of force constant k = 200 N/m is attached to a 700-g mass oscillating between x = 1.2 and x = 2.4 meters. What is the speed of the mass when it is at the 1.5 meter point?

88 Sample problem. A 2.0-kg mass attached to a spring oscillates with an amplitude of 12.0 cm and a frequency of 3.0 Hz. What is its total energy?

89 Pendulums The pendulum can be thought of as a simple harmonic oscillator. The displacement needs to be small for it to work properly.

90 Pendulum Forces θ T mg sinθ θ mg

91 Period of a pendulum T = 2 π l g T: period (s) l: length of string (m) g: gravitational acceleration (m/s 2 )

92 Sample problem Predict the period of a pendulum consisting of a 500 gram mass attached to a 2.5-m long string.

93 Sample problem Suppose you notice that a 5-kg weight tied to a string swings back and forth 5 times in 20 seconds. How long is the string?

94 Sample problem The period of a pendulum is observed to be T. Suppose you want to make the period 2T. What do you do to the pendulum?