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Sound Mark Lesmeister Dawson High School Physics This presentation is intended solely for use by Dawson High School Pre-AP Physics students.

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SECTION 1: INTRODUCTION TO SOUND

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Nature of Sound Waves Sound waves are the result of vibrating molecules of air, water or other medium. Sound waves are longitudinal waves. Animation courtesy Dan Russell, Kettering University

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Nature of Sound Waves Sound waves are the result of vibrating molecules of air, water or other medium. Sound waves are longitudinal waves. Motion of the medium is parallel to direction of travel of the wave. Sound waves consist of compressions and rarefactions. Compression Is to Rarefaction Crest Is to Trough High density Is to Low density as

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Nature of Sound Waves Sound waves are the result of vibrating molecules of air, water or other medium. Sound waves are longitudinal waves. Sound waves spread out in three dimensions. Animation courtesy Dan Russell, Kettering University

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Frequency of sound waves The frequency of an audible sound wave is related to its pitch. Sound waves vary greatly in frequency. Sound Waves Infrasonic 20 Hz 20,000 Hz

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Frequency of sound waves 20 Hz 80 Hz 160 Hz 220 Hz 440 Hz 880 Hz 2200 Hz 4400 Hz 8800 Hz 13200 Hz 22000 Hz

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Use of Ultrasonic Waves Ultrasonic waves can be used to produce ultrasound images of objects inside the body. These images do not involve harmful X-rays. The size of the ultrasonic wavelength limits the size of objects that can be seen.

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Warning: The next slide shows an image of a 28 weeks gestational age fetus.

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4-d Ultrasound Image Source: Wikipedia

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PART 2: THE MATHEMATICS OF SOUND

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The Speed of Sound The speed of sound depends on the medium. Animation courtesy Dan Russell, Kettering University

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The Speed of Sound The speed of sound depends on the medium. The more rigid the medium, the faster sound travels through it. The temperature of the medium may affect the speed of sound. The speed of sound of some common materials is given on page 482. Air: 331 m/s at 0 o C, 346 m/s at 25 o C Water: 1490 m/s at 25 o C Metals: Al- 5100 m/s, Cu- 3560 m/s

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Mach Numbers The speed of sound in air is also known as Mach 1. A plane flying at Mach 2 is flying twice the speed of sound. The shuttle flies at a speed of about Mach 25.

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Sound Application Questions: Marine Mammals Dolphins can produce sound waves with frequencies from 250 Hz to 220 kHz, but use only the higher frequencies for echolocation. Why? Dolphin sound pulses travel through 20 o C ocean water at 1450 m/s, but through 20 o C air at only 343 m/s. What explains the difference? As a dolphin swims toward a fish, the frequency of the reflected pulses is higher than the transmitted pulses. Is the dolphin catching up to the fish or falling behind?

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Marine Mammal Discussion Question SONAR is the use of sound as a means of detecting objects. Active SONAR systems send out pulses of sound, the reflections of which are then received and interpreted. Active sonar systems have been implicated in a small number of strandings of marine mammals. Small means about 5 strandings per year (some of which involved more than in animal), compared to 3,600 strandings/year from natural causes or 600,000 accidental deaths/year due to the commercial fishing industry. Should peacetime use of SONAR be banned in order to prevent these strandings?

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The Doppler Effect

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The Doppler Effect: Waves from a Moving Source v=f so a smaller wavelength means a higher frequency. Animation courtesy Dan Russell, Kettering University

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The Doppler Effect: Waves as seen by a moving observer. Animation courtesy Dan Russell, Kettering University

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The Doppler Effect

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Motion of either the source or the observer of a wave causes the frequency to shift. If the relative motion results in more wave crests reaching the observer per second, the frequency is increased. If the relative motion results in fewer wave crests reaching the observer per second, the frequency is decreased.

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Calculating Doppler Effect: Moving Observer A moving observer will detect additional wavefronts per second because of the motion.

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Calculating the Doppler Effect: Moving Source dd

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Doppler Effect Use the upper signs when the objects are moving toward each other, and the bottom signs when they are moving away.

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Sound Intensity All waves transfer energy. Power is the rate of energy transfer. Intensity is the rate of energy transfer through a unit of area. In general, For a spherical wave, Courtesy of Dr. Dan Russell, Kettering University 2008 by W.H. Freeman and Company

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Calculating Intensity P = power r = distance from the source. Intensity is measured in W/m 2. What is the intensity of sound waves from an electric guitar at a distance of 5.0 m when its power output is 0.50 W? 1.6 x 10 -3 W/m 2

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Interpreting Intensity Intensity and frequency determine which sounds are audible. The threshold of hearing has frequencies around 1000 Hz and intensities of 1.0 x10 -12 W/m 2. The threshold of pain occurs at about 1.0 W/m 2. 1.0 x 10 -12 W/m 2 1.0 W/m 2

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Range of Hearing Diagram from Holt Physics, Holt, Reinhart and Winston 2002.

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Loudness and Decibel level The intensity of a sound is related to its loudness or volume. When intensity increases by a factor of 10, loudness approximately doubles. X 10 in intensity means X2 in loudness. A decibel level relates the intensity of a sound to the threshold of hearing intensity. The decibel scale is based on powers of 10. X 10 in intensity means + 10 dB

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Decibel level dB LevelIncrease inApproximate Intensity loudness increase 10 dB 10 X2 X 20100 X 4 X 301000 X8 X

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Table taken from Holt Physics, Holt, Reinhart and Winston 2002.

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Decibel Calculations Example 1: A certain loudspeaker doubles the intensity of a sound wave. What is the corresponding dB increase? Example 2: What is the intensity of a 75 dB sound wave if the reference level is 10 -12 W/m 2 ?

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SOUND PHENOMENA

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Warm-up: Discovery Lab Activity Hold the tube vertically, so that it is partially submerged in the water in the cup. Strike the tuning fork and place it over the top of the tube. Slowly change the position of the tube, up and down, and listen for any changes in the sound.

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Resonance Many systems have a natural frequency of vibration; for example Simple harmonic oscillators Pendulum Mass and spring system Piano strings, other musical instruments. Resonance occurs when the frequency of a force applied to a system matches the natural frequency of vibration of the systems. A resonance will result in a large amplitude of vibration.

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Standing Waves and Harmonics When certain systems, such as strings or air columns, are vibrated, standing waves are produced. Only standing waves of certain frequencies are possible. Those frequencies are called harmonics of the system.

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Standing Waves on a String A stretched string will produce harmonics with wavelengths that will fit on the string. If L is the length of the string, the allowed wavelengths are 2L, L, (2/3)L, (1/2)L, etc. Graphic from Holt Physics Holt, Reinhart and Winston 2002.

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Harmonic Series of Standing Waves: Vibrating String

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Standing Waves in an Air Column Standing waves can be set up in an air column. A closed end of an air column will always be a node. An open end of an air column will always be an antinode of a standing wave.

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Harmonic Series of Standing Waves: Pipe Open at Both Ends Graphic from Holt Physics Holt, Reinhart and Winston 2002. Flutes and similar instruments are modeled as pipes open at both ends.

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Harmonic Series of Standing Waves: Pipe Open at Both Ends Graphic from Holt Physics Holt, Reinhart and Winston 2002.

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Harmonic Series: Pipe Closed at One End Graphic from Holt Physics Holt, Reinhart and Winston 2002. Clarinets and brass instruments can be modeled as pipes closed at one end.

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Harmonic Series: Pipe Closed at One End Graphic from Holt Physics Holt, Reinhart and Winston 2002.

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Harmonics and Wind Instruments Other reed instruments such as saxophones, oboes and bassoons, although they are closed at one end, behave more like a cone than a cylinder. The result is that their resonances are closer to a pipe open at both ends.

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Harmonics and Timbre Sounds with the same frequency can sound quite different. The difference is the result of the presence of different harmonics at different intensities. The characteristics of a musical note that result from the different harmonics it contains are called timbre. The fundamental frequency determines the pitch of the sound.

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Sample Timbres 440 Hz tone 440 Hz and 880 Hz First 5 harmonics of 440 Hz, each with intensity of previous one. First 5 odd harmonics of 440 Hz, each with intensity of previous one. Clarinet playing scale.

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Beats Sound waves of slightly different frequencies produce beats. 440 Hz and 441 Hz together Beats are the result of constructive and destructive interference. The frequency of the beats is equal to the difference in frequency of the two sound waves. 440 Hz and 442 Hz together.

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Some Musical Intervals Unison- e.g. middle C and middle C A note with the same frequency. Octave- e.g. middle C and high C A note with double the frequency. The first harmonic of this note equals the second harmonic of the original note. Fifth- e.g. C and G A note with 3/2 the frequency. The second harmonic of this note equals the 3 rd harmonic of the original note. Fourth- e.g. C and F A note with 4/3 the frequency. The third harmonic of this note equals the fourth harmonic of the original note.