2. Waves and Sound AP Physics 1 Conroe High School

3. Wave Motion A wave is, in general, a disturbance that moves through a medium.

4. A wave carries energy from one location to another without transporting the material of the medium. Examples of mechanical waves include water waves, waves on a string, and sound waves.

5. What is a wave A WAVE is a vibration or disturbance in space. A MEDIUM is the substance that all SOUND WAVES travel through and need to have in order to move.

6. What is the medium? Water Slinky

7. Transverse and Longitudinal Waves There are two types of mechanical waves: Transverse waves: The particles of the medium vibrate up and down (perpendicular to the wave).

8. Longitudinal waves: The particles in the medium vibrate along the same direction as the wave (parallel). The medium undergoes a series of expansions and compressions. The expansions are when the coils are far apart and compressions are when they are when the coil is close together. Expansions and compressions are the analogs of the crests and troughs of a transverse wave.

9. Longitudinal waves:

10. Longitudinal Longitudinal Wave - A fixed point will move parallel with the wave motion 2 areas Compression- an area of high molecular density and pressure Rarefaction - an area of low molecular density and pressure

12. Transverse Wave - A fixed point will move perpendicular with the wave motion. Transverse Wave parts(recall demo for simple harmonic motion )- crest, trough, wavelength, amplitude, frequency, period

14. PARTS OF A WAVE

16. Amplitude: maximum displacement from equilibrium Crest: Top part of the wave Trough: Bottom part of the wave Wavelength: Length from crest to crest or trough to trough

17. Velocity and Wave Frequency. The period T is the time to move a distance of one wavelength. Therefore, the wave speed is: The frequency f is in s -1 or hertz (Hz). The velocity of any wave is the product of the frequency and the wavelength:

18. On a string with tension F T and mass per unit length of the string (linear density) m/L the velocity (m/s) of the wave is:

19. Wave Speed You can find the speed of a wave by multiplying the wave’s wavelength in meters by the frequency (cycles per second). Since a “cycle” is not a standard unit this gives you meters/second.

20. 9.1 Measurements show that the wavelength of a sound wave in a certain material is 18.0 cm. The frequency of the wave is 1900 Hz. What is the speed of the sound wave? λ = 0.18 m f = 1900 Hz v = λ f = 0.18 (1900) = 342 m/s

21. 9.2 A horizontal cord 5.00 m long has a mass of 1.45 g. a. What must be the tension in the cord if the wavelength of a 120 Hz wave is 60 cm? L = 5 m m = 1.45x10 -3 kg f = 120 Hz λ = 0.6 m = 1.5 N v = λ f = 0.6 (120) = 72 m/s

22. b. How large a mass must be hung from its end to give it this tension? F T = F G = mg = 0.153 kg

23. Example A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along a rope in 10.0 s. What is the wavelength? 0.0319 m

24. REFLECTION A wave front of a wave striking a straight barrier follows the law of reflection. This law states that: "The angle of incidence equals the angle of reflection". The angle of incidence is the angle between the direction of the incoming wave and a normal drawn to the surface. The angle of reflection is the angle between the direction of the reflected wave and the normal to the surface.

25. Reflection (bounce)

26. Reflection The law of reflection: the angle of incidence equals the angle of reflection NOTE: Angles in optics are taken from the normal line to the surface

28. Used to locate underwater objects and distances. ***Reflection**

30. Echolocation

31. BEHAVIOR OF WAVES When a wave travels from one medium to another, the wave is both reflected and transmitted. When a wave passes into a new medium, its speed changes. The wave must have the same frequency in the new medium as in the old medium, thus, the wavelength adjusts.

36. REFRACTION A water wave traveling from deep water into shallow water changes direction. This phenomenon is known as refraction.

37. Refraction (bend)

42. Refraction of Waves refraction - The speed of a water wave increases with depth. This change in speed is accompanied by refraction. This effect is a consequence of the wave equation, v = ƒ. Since ƒ is constant, a decrease in v produces a decrease in.

45. Interference: What happens when two waves pass through the same region? When two crests overlap it is called constructive interference. The resultant displacement is larger then the individual ones. When a crest and a trough interfere, it is called destructive interference. The resultant displacement is smaller.

46. Interference when two waves are combined, either constructive or destructive interference can occur. __________ interference ____________ interference

47. Constructive Interference

48. Destructive Interference

50. Noise canceling head phones for flights Uses complete destructive interference

52. DIFFRACTION Waves tend to bend as they pass an obstacle. For example, water waves passing a log in a river will tend to bend around the log after they pass. This bending is known as diffraction. The amount of diffraction depends on the wavelength and the size of the obstacle.

53. Diffraction of Waves. When a traveling water wave hits an obstacle, the wavefronts spreads out round the edge and becomes curved. This phenomenon refers to diffraction. The wavelength of the wave is not changed in diffraction.

56. Diffraction

57. Small openings cause diffraction, even curved waves will diffract

58. Two openings will allow diffracted waves to interfere with each other.

60. Standing Waves A standing wave is produced when a wave that is traveling is reflected back upon itself. There are two main parts to a standing wave: Antinodes – Areas of MAXIMUM AMPLITUDE Nodes – Areas of ZERO AMPLITUDE.

61. STANDING WAVES IN STRINGS At certain frequencies standing waves can be produced in which the waves seem to be standing still rather than traveling. This means that the string is vibrating as a whole. This is called resonance and the frequencies at which standing waves occur are called resonant frequencies or harmonics.

62. A standing wave is produced by the superposition of two periodic waves having identical frequencies and amplitudes which are traveling in opposite directions. In stringed musical instruments, the standing wave is produced by waves reflecting off a fixed end and interfering with oncoming waves as they travel back through the medium.

63. Second Harmonic

64. Third Harmonic

65. The points of destructive interference (no vibration) are called nodes, and the points of constructive interference (maximum amplitude of vibration) are called antinodes.

66. When a wave reflects off of something, it can interfere with its own reflection. The interference is alternately constructive or destructive as the two waves move past each other. This creates a standing wave.

67. There can be more than one frequency for standing waves. Frequencies at which standing waves can be produced are called the natural (or resonant) frequencies. When a string on an instrument is plucked, vibrations, that is, waves, travel back and forth through the medium being reflected at each fixed end. Certain sized waves can survive on the medium. These certain sized waves will not cancel each other out as they reflect back upon themselves. These certain sized waves are called the harmonics of the vibration. They are standing waves. That is, they produce patterns which do not move.plucked

69. Standing Waves in Strings A string can be fixed in both sides, like a guitar or piano string.When the string is plucked, many frequency waves will travel in both directions. Most will interfere randomly and die away. Only those with resonant frequencies will persist. Since the ends are fixed, they will be the nodes. The wavelengths of the standing waves have a simple relation to the length of the string. The lowest frequency called the fundamental frequency has only one antinode. That corresponds to half a wavelength:

70. The other natural frequencies are called overtones. They are also called harmonics and they are integer multiples of the fundamental. The fundamental is called the first harmonic. The next frequency has two antinodes and is called the second harmonic.

71. 9.3 A metal string is under a tension of 88.2 N. Its length is 50 cm and its mass is 0.500 g. a. Find the velocity of the waves on the string. m = 5x10 -4 kg F T = 88.2 N L = 0.5 m = 297 m/s b. Determine the frequencies of its fundamental, first overtone and second overtone. Fundamental: L = 1/2 λ λ = 2L = 2(0.5) = 1 m = 297 Hz

72. First overtone f n = n f' f 2 = 2(297) = 594 Hz Second overtone f n = n f' f 3 = 3(297) = 891 Hz

73. 9.4 A string 2.0 m long is driven by a 240 Hz vibrator at its end. The string resonates in four segments. What is the speed of the waves on the string? L = 2 m f = 240 Hz 4 segments: 4th Harmonic L = 4/2 λ = 2 λ λ = ½ L = ½ (2) = 1 m v = f λ = 240 (1) = 240 m/s

74. 9.5 A banjo string 30 cm long resonates in its fundamental to a frequency of 256 Hz. What is the speed of the waves on the string? L = 0.3 m f = 256 Hz Fundamental: L = ½ λ λ = 2L = 2(0.3) = 0.6 m v = f λ = 256 (0.6) = 154 m/s

75. 9.6 A string vibrates in five segments to a frequency of 460 Hz. a. What is its fundamental frequency? f 5 = 460 Hz f n = n f' = 92 Hz b. What frequency will cause it to vibrate in three segments? f n = n f' f 3 = 3(92) = 276 Hz

76. SOUND WAVES Sound is a longitudinal wave produced by a vibration that travels away from the source through solids, liquids, or gases, but not through a vacuum. The speed of sound is independent of the pressure, frequency, and wavelength of the sound. However, the speed of sound in a gas is proportional to the temperature T. The following equation is useful in determining the speed of sound in air v = 331 + 0.6 T Units: m/s Where 331 is the speed of sound in m/s at 0°C, and T is the temperature in °C

77. Tuning fork creating a sound wave Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com

78. Sound is a pressure wave Animations courtesy of Paul Hewitt and borrowed from physicsclassroom.com

79. Sound Waves Sound Waves are a common type of standing wave as they are caused by RESONANCE. Resonance – when a FORCED vibration matches an object’s natural frequency thus producing vibration, sound, or even damage. One example of this involves shattering a wine glass by hitting a musical note that is on the same frequency as the natural frequency of the glass. (Natural frequency depends on the size, shape, and composition of the object in question.) Because the frequencies resonate, or are in sync with one another, maximum energy transfer is possible.

80. There are two main characteristic of sound: pitch and loudness. Pitch refers to how high (or low) the sound is. It is measured by the frequency. We hear frequencies in the range of 20 Hz to 20,000 Hz. This is called the audible range. Frequencies above this range are called ultrasonic. Sound waves whose frequency is lower than the audible range are called infrasonic.

81. Sound Waves The production of sound involves setting up a wave in air. To set up a CONTINUOUS sound you will need to set a standing wave pattern. Three LARGE CLASSES of instruments Stringed - standing wave is set up in a tightly stretched string Percussion - standing wave is produced by the vibration of solid objects Wind - standing wave is set up in a column of air that is either OPEN or CLOSED Factors that influence the speed of sound are density of solids or liquid, and TEMPERATURE

82. INTERFERENCE OF SOUND WAVES: BEATS If two sources are close in frequency, the sound from them interferes and what we hear is an alternating sound level. The level rise and falls. If the alternating sound is regular, it is called beats.

83. The beat frequency equals the difference in frequencies between the sources. This is a way to tune musical instruments. Compare a tuning fork to a note and tune until the beats disappear. CI Constructive Interference DI Destructive Interference

84. HUMAN EAR: The ear consists of three basic parts: Outer ear: serves to collect and channel sound to the middle ear. Middle ear: serves to transform the energy of a sound wave into the internal vibrations of the bone structure of the middle ear and transform these vibrations into a compressional wave in the inner ear. Inner ear: serves to transform the energy of a compressional wave within the inner ear fluid into nerve impulses which can be transmitted to the brain.

86. Hearing: A compression forces the eardrum inward and an expansion forces the eardrum outward, thus vibrating the eardrum at the same frequency of the sound wave.

87. SOURCES OF SOUND Sound comes from a vibrating object. If an object vibrates with frequency and intensity within the audible range, it produces sound we can hear. MUSICAL INSTRUMENTS - String Instruments: guitar, violin and piano -Wind Instruments: Open Pipe: flute and some organ pipes Closed Pipe: clarinet,oboe and saxophone

88. STRING INSTRUMENTS The sounds produced by vibrating strings are not very loud. Many stringed instruments make use of a sounding board or box, sometimes called a resonator, to amplify the sounds produced. The strings on a piano are attached to a sounding board while for guitar strings a sound box is used. When the string is plucked and begins to vibrate, the sounding board or box begins to vibrate as well. Since the board or box has a greater area in contact with the air, it tends to amplify the sounds. On a guitar or a violin, the length of the strings are the same, but their mass per length is different. That changes the velocity and so the frequency changes.

89. WIND INSTRUMENTS Wind instruments produce sound from the vibrations of standing waves in columns of air inside a pipe or a tube. In a string, the ends are nodes. In air columns the ends can be either nodes or antinodes. Open pipe

90. Open Pipes OPEN PIPES- have an antinode on BOTH ends of the tube. What is the SMALLEST length of pipe you can have to hear a sound? You will get your FIRST sound when the length of the pipe equals one-half of a wavelength.

91. Open Pipes - Harmonics Since harmonics are MULTIPLES of the fundamental, the second harmonic of an “open pipe” will be ONE WAVELENGTH. The picture above is the SECOND harmonic or the FIRST OVERTONE.

92. Open pipes - Harmonics Another half of a wavelength would ALSO produce an antinode on BOTH ends. In fact, no matter how many halves you add you will always have an antinode on the ends The picture above is the THIRD harmonic or the SECOND OVERTONE. CONCLUSION: Sounds in OPEN pipes are produced at ALL HARMONICS!

93. Possible Waves for Open Pipe L Fundamental, n = 11st Overtone, n = 22nd Overtone, n = 33rd Overtone, n = 4 All harmonics are possible for open pipes:

94. Characteristic Frequencies for an Open Pipe. L Fundamental, n = 11st Overtone, n = 22nd Overtone, n = 33rd Overtone, n = 4 All harmonics are possible for open pipes:

95. Half Closed Pipe

96. Closed Pipes - Harmonics Harmonics are MULTIPLES of the fundamental frequency. In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NO SOUND is produced

97. Closed Pipes - Harmonics In a closed pipe you have an ANTINODE at the 3rd harmonic position, therefore SOUND is produced. CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS!

98. Possible Waves for Closed Pipe. Fundamental, n = 1 1st Overtone, n = 3 2nd Overtone, n = 5 3rd Overtone, n = 7 Only the odd harmonics are allowed: L

99. Possible Waves for Closed Pipe. Fundamental, n = 1 1st Overtone, n = 3 2nd Overtone, n = 5 3rd Overtone, n = 7 Only the odd harmonics are allowed: L

100. Example The speed of sound waves in air is found to be 340 m/s. Determine the fundamental frequency (1st harmonic) of an open-end air column which has a length of 67.5 cm. 251.85 HZ

101. Example The windpipe of a typical whooping crane is about 1.525-m long. What is the lowest resonant frequency of this pipe assuming it is a pipe closed at one end? Assume a temperature of 37°C. 353.2 m/s 57.90 Hz

102. a) For open pipe The overtones will be multiples of the fundamental b) For closed pipe The overtones will be the odd multiples of the fundamental HARMONICS

103. 9.7 A saxophone plays a tune in the key of B-flat. The saxophone has a third harmonic frequency of 466.2 Hz when the speed of sound in air is 331 m/s. What is the length of the pipe that makes up the saxophone? n = 3 f 3 = 466.2 Hz v = 331 m/s f' = f 3 /n = 466.2/3 = 155.4 Hz Saxophone is closed so: L= 1/4 λ = 0.53 m

104. 9.8 An organ pipe that is open at both ends has a fundamental frequency of 370.0 Hz when the speed of sound in air is 331 m/s. What is the length of this pipe? L= 1/2 λ f' = 370 Hz v = 331 m/s = 0.447 m

105. 9.9 What is the fundamental frequency of a viola string that is 35.0 cm long when the speed of waves on this string is 346 m/s? L = 0.35 m v = 346 m/s L= 1/2 λ and λ = 2L = 494.2 Hz

106. 9.10 A pipe that is open at both ends has a fundamental frequency of 125 Hz. If the pipe is 1.32 m long, what is the speed of the waves in the pipe? f' = 125 Hz L = 1.32 m L= 1/2 λ and λ = 2L v = λ f =2 L f = 2(1.32)(125) = 330 m/s

107. 9.11 A pipe that is closed on one end has a seventh harmonic frequency of 466.2 Hz. If the pipe is 1.53 m long, what is the speed of the waves in the pipe? n = 7 f 7 = 466.2 Hz L = 1.53 m L= 7/4 λ and λ = 4/7 L = 407.6 m/s

108. What length of closed pipe is needed to resonate with a fundamental frequency of 256 Hz? What is the second overtone? Assume that the velocity of sound is 340 M/s. Closed pipe AN L = ? L = 33.2 cm The second overtone occurs when n = 5: f 5 = 5f 1 = 5(256 Hz) 2nd Ovt. = 1280 Hz

109. DOPPLER EFFECT When a source of sound waves and a listener approach one another, the pitch of the sound is increased as compared to the frequency heard if they remain at rest. If the source and the listener recede from one another, the frequency is decreased. This phenomenon is known as the Doppler effect.

110. __________________________

111. Doppler Effect Apparent change in frequency (pitch) of a sound from a moving source.Apparent change in frequency (pitch) of a sound from a moving source.

112. *Moving towards increases the pitch *Moving away decreases the pitch *Think of sirens

114. Doppler Radar

115. Light waves also exhibit the Doppler effect. The spectra of stars that are receding from us is shifted toward the longer wavelengths of light. This is known as the red shift. Measurement of the red shift allows astrophysicists to calculate the speed at which stars are moving away. Since almost all stars and galaxies exhibit a red shift, it is believed that the universe is expanding.

118. SHOCK WAVES AND THE SONIC BOOM When the speed of a source of sound exceeds the speed of sound, the sound waves in front of the source tend to overlap and constructively interfere. The superposition of the waves produce an extremely large amplitude wave called a shock wave. The shock wave contains a great deal of energy. When the shock wave passes a listener, this energy is heard as a sonic boom. The sonic boom is heard only for a fraction of a second; however, it sounds as if an explosion has occurred and can cause damage.

119. Test Review Superposition is constructive and destructive interference. Look at the wave, find the amplitudes at all 4 points.

120. Find angle of incidence

121. What is about to happen?

123. What causes this? Why does it happen?

124. What is going on here?