DOCSLIB.ORG

Ch 12: Sound Medium Vs Velocity

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Ch 12: Sound Medium vs velocity • Sound is a compression wave (longitudinal) which needs a medium to compress. A wave has regions of high and low pressure. • Speed- different for various materials. Depends on the elastic modulus, B and the density, ρ of the material. v B/ • Speed varies with temperature by: v (331 0.60T)m/s • Here we assume t = 20°C so v=343m/s Sound perceptions • A listener is sensitive to 2 different aspects of sound: Loudness and Pitch. Each is subjective yet measureable. • Loudness is related to Energy of the wave • Pitch (highness or lowness of sound) is determined by the frequency of the wave. • The Audible Range of human hearing is from 20Hz to 20,000Hz with higher frequencies disappearing as we age. Beyond hearing • Sound frequencies above the audible range are called ultrasonic (above 20,000 Hz). Dogs can detect sounds as high as 50,000 Hz and bats as high as 100,000 Hz. Many medicinal applications use ultrasonic sounds. • Sound frequencies below 20 Hz are called infrasonic. Sources include earthquakes, thunder, volcanoes, & waves made by heavy machinery. Graphical analysis of sound • We can look at a compression (pressure) wave from a perspective of displacement or of pressure variations. The waves produced by each are ¼ λ out of phase with each other. Sound Intensity • Loudness is a sensation measuring the intensity of a wave. • Intensity = energy transported per unit time across a unit area. I≈A2 • Intensity (I) has units power/area = watt/m2 • Human ear can detect I from 10-12 w/m2 to 1w/m2 which is a wide range! • To make a sound twice as loud requires 10x the intensity. • In the open sound intensity follows inverse square law as you get farther from the source. Decibels, dB • We measure sound intensity levels, β using a logarithmic scale having a unit of bels. • 1 decibel, dB is 0.1 bel (10dB =1bel) -12 2 • I0 is the minimum intensity audible (1x10 W/m ) and the log is base 10, so we define intensity level as I 10log I0 • The threshold of hearing would be 0dB • Each 10dB increase is 10x the intensity. (20dB = 100x intensity of 0dB; 30dB = 1000x >0dB) Vibrating Strings • Recall how standing waves are made on a string… • Fundamental- pitch determined by lowest resonant frequency where nodes are only at the ends. Here λ=2L so v=f/2L on the string. • Strings on some instruments are the same length, but sound different b/c each has a different m/L which effects velocity: v FT /(m/L) • Adjusting tension is how we tune the instrument • Velocity on a heavy string is less and f will be less for the same λ. Ex 12-6 Piano strings • The highest key on a piano corresponds to a frequency about 150 times that of the lowest key. If the string of the highest note is 5.0cm long, how long would the string for the lowest note be if it had the same mass per length and was under the same tension? • Solution: The velocity would be the same on each string so the frequency is inversely proportional to the length L of the string (f=v/λ= v/2L) Solution cont’d L f • Thus L H where the subscripts L and H refer to low L H f L and high notes. It follows that LL LH ( f H / fL ) (5.0cm)(150) 750cm 7.5m • This would be too long for a piano so the longer lower strings are made heavier to avoid this. Amplification • Stringed instruments need a ‘sounding board’ to help amplify the sound by putting a greater surface area in contact with the air. This produces a stronger wave. • Other instruments use a column of air to set up a standing wave. • The fundamental frequency on a string has antinodes at both ends and a single anti node. Harmonics or overtones are whole # multiples of the fundamental. pipes • In a pipe the air is vibrating forming the standing wave • We can discuss the waves by the air displacement OR by the pressure in the air. (Recall these are separated by ¼ a λ) • We can have pipes that are open at both ends (called open tubes) or that are closed at one end (closed tube). • Read last paragraph on pg 358- first 2 on page 359 about air displacement on open tubes like a flute. Pipe diagrams Ex 12-8 open & closed organ pipes • What will be the fundamental frequency and first three overtones for a 26cm long organ pipe at 20°C if it is (a) open and (b) closed? • Solution: At 20°C, the speed of sound in air is 343m/s. • (a) For an open pipe, the fundamental frequency is v 343m /s f 660Hz 1 2L 2(0.26m) • The next 3 overtones would be 1320 Hz, 1980 Hz, 2640 Hz and so on… • (b) For a closed pipe, the fundamental is v 343m /s f 330Hz 1 4L 4(0.26m) • The next 3 overtones will only be heard at odd multiples so we have 990Hz, 1650 Hz, and 2310 Hz Interference- beats • As two or more waves superimpose, their amplitudes add algebraically. • We have constructive interference when waves are in phase and destructive when out of phase. • Beats occur when sound waves have frequencies close but different. As the waves interact a listener perceives sound levels that alternately rise and fall. • Beat frequency is found as the difference between the 2 waves. • A 400 Hz tone and a 396 Hz tone will have a fbeat=4Hz Doppler effect • Recall wave speed depends only on medium. • If a source or listener move relative to a wave, the wave frequency (and therefore wavelength) can be perceived to change resulting in a change in pitch. Perceived frequency • The shift in wavelength is directly proportional to the speed of the source, vs. • The new frequency, f ’ will then be: f f v • 1 s for a source moving toward you • v this is called blue shift f f v • 1 s for a source moving away (red shift) v Doppler effect in space Your turn to prac • Please do Ch 12 Review pgs 375-378 • Problems # 4, 29, 36, 48, 55 • 1998 FRQ B5 .
Recommended publications
  • Lab 12. Vibrating Strings

    Lab 12. Vibrating Strings

    Lab 12. Vibrating Strings Goals • To experimentally determine the relationships between the fundamental resonant frequency of a vibrating string and its length, its mass per unit length, and the tension in the string. • To introduce a useful graphical method for testing whether the quantities x and y are related by a “simple power function” of the form y = axn. If so, the constants a and n can be determined from the graph. • To experimentally determine the relationship between resonant frequencies and higher order “mode” numbers. • To develop one general relationship/equation that relates the resonant frequency of a string to the four parameters: length, mass per unit length, tension, and mode number. Introduction Vibrating strings are part of our common experience. Which as you may have learned by now means that you have built up explanations in your subconscious about how they work, and that those explanations are sometimes self-contradictory, and rarely entirely correct. Musical instruments from all around the world employ vibrating strings to make musical sounds. Anyone who plays such an instrument knows that changing the tension in the string changes the pitch, which in physics terms means changing the resonant frequency of vibration. Similarly, changing the thickness (and thus the mass) of the string also affects its sound (frequency). String length must also have some effect, since a bass violin is much bigger than a normal violin and sounds much different. The interplay between these factors is explored in this laboratory experi- ment. You do not need to know physics to understand how instruments work. In fact, in the course of this lab alone you will engage with material which entire PhDs in music theory have been written.
  • The Physics of Sound 1

    The Physics of Sound 1

    The Physics of Sound 1 The Physics of Sound Sound lies at the very center of speech communication. A sound wave is both the end product of the speech production mechanism and the primary source of raw material used by the listener to recover the speaker's message. Because of the central role played by sound in speech communication, it is important to have a good understanding of how sound is produced, modified, and measured. The purpose of this chapter will be to review some basic principles underlying the physics of sound, with a particular focus on two ideas that play an especially important role in both speech and hearing: the concept of the spectrum and acoustic filtering. The speech production mechanism is a kind of assembly line that operates by generating some relatively simple sounds consisting of various combinations of buzzes, hisses, and pops, and then filtering those sounds by making a number of fine adjustments to the tongue, lips, jaw, soft palate, and other articulators. We will also see that a crucial step at the receiving end occurs when the ear breaks this complex sound into its individual frequency components in much the same way that a prism breaks white light into components of different optical frequencies. Before getting into these ideas it is first necessary to cover the basic principles of vibration and sound propagation. Sound and Vibration A sound wave is an air pressure disturbance that results from vibration. The vibration can come from a tuning fork, a guitar string, the column of air in an organ pipe, the head (or rim) of a snare drum, steam escaping from a radiator, the reed on a clarinet, the diaphragm of a loudspeaker, the vocal cords, or virtually anything that vibrates in a frequency range that is audible to a listener (roughly 20 to 20,000 cycles per second for humans).
  • The Musical Kinetic Shape: a Variable Tension String Instrument

    The Musical Kinetic Shape: a Variable Tension String Instrument

    The Musical Kinetic Shape: AVariableTensionStringInstrument Ismet Handˇzi´c, Kyle B. Reed University of South Florida, Department of Mechanical Engineering, Tampa, Florida Abstract In this article we present a novel variable tension string instrument which relies on a kinetic shape to actively alter the tension of a fixed length taut string. We derived a mathematical model that relates the two-dimensional kinetic shape equation to the string’s physical and dynamic parameters. With this model we designed and constructed an automated instrument that is able to play frequencies within predicted and recognizable frequencies. This prototype instrument is also able to play programmed melodies. Keywords: musical instrument, variable tension, kinetic shape, string vibration 1. Introduction It is possible to vary the fundamental natural oscillation frequency of a taut and uniform string by either changing the string’s length, linear density, or tension. Most string musical instruments produce di↵erent tones by either altering string length (fretting) or playing preset and di↵erent string gages and string tensions. Although tension can be used to adjust the frequency of a string, it is typically only used in this way for fine tuning the preset tension needed to generate a specific note frequency. In this article, we present a novel string instrument concept that is able to continuously change the fundamental oscillation frequency of a plucked (or bowed) string by altering string tension in a controlled and predicted Email addresses: [email protected] (Ismet Handˇzi´c), [email protected] (Kyle B. Reed) URL: http://reedlab.eng.usf.edu/ () Preprint submitted to Applied Acoustics April 19, 2014 Figure 1: The musical kinetic shape variable tension string instrument prototype.
  • An Experiment in High-Frequency Sediment Acoustics: SAX99

    An Experiment in High-Frequency Sediment Acoustics: SAX99

    An Experiment in High-Frequency Sediment Acoustics: SAX99 Eric I. Thorsos1, Kevin L. Williams1, Darrell R. Jackson1, Michael D. Richardson2, Kevin B. Briggs2, and Dajun Tang1 1 Applied Physics Laboratory, University of Washington, 1013 NE 40th St, Seattle, WA 98105, USA [email protected], [email protected], [email protected], [email protected] 2 Marine Geosciences Division, Naval Research Laboratory, Stennis Space Center, MS 39529, USA [email protected], [email protected] Abstract A major high-frequency sediment acoustics experiment was conducted in shallow waters of the northeastern Gulf of Mexico. The experiment addressed high-frequency acoustic backscattering from the seafloor, acoustic penetration into the seafloor, and acoustic propagation within the seafloor. Extensive in situ measurements were made of the sediment geophysical properties and of the biological and hydrodynamic processes affecting the environment. An overview is given of the measurement program. Initial results from APL-UW acoustic measurements and modelling are then described. 1. Introduction “SAX99” (for sediment acoustics experiment - 1999) was conducted in the fall of 1999 at a site 2 km offshore of the Florida Panhandle and involved investigators from many institutions [1,2]. SAX99 was focused on measurements and modelling of high-frequency sediment acoustics and therefore required detailed environmental characterisation. Acoustic measurements included backscattering from the seafloor, penetration into the seafloor, and propagation within the seafloor at frequencies chiefly in the 10-300 kHz range [1]. Acoustic backscattering and penetration measurements were made both above and below the critical grazing angle, about 30° for the sand seafloor at the SAX99 site.
  • AN INTRODUCTION to MUSIC THEORY Revision A

    AN INTRODUCTION to MUSIC THEORY Revision A

    AN INTRODUCTION TO MUSIC THEORY Revision A By Tom Irvine Email: [email protected] July 4, 2002 ________________________________________________________________________ Historical Background Pythagoras of Samos was a Greek philosopher and mathematician, who lived from approximately 560 to 480 BC. Pythagoras and his followers believed that all relations could be reduced to numerical relations. This conclusion stemmed from observations in music, mathematics, and astronomy. Pythagoras studied the sound produced by vibrating strings. He subjected two strings to equal tension. He then divided one string exactly in half. When he plucked each string, he discovered that the shorter string produced a pitch which was one octave higher than the longer string. A one-octave separation occurs when the higher frequency is twice the lower frequency. German scientist Hermann Helmholtz (1821-1894) made further contributions to music theory. Helmholtz wrote “On the Sensations of Tone” to establish the scientific basis of musical theory. Natural Frequencies of Strings A note played on a string has a fundamental frequency, which is its lowest natural frequency. The note also has overtones at consecutive integer multiples of its fundamental frequency. Plucking a string thus excites a number of tones. Ratios The theories of Pythagoras and Helmholz depend on the frequency ratios shown in Table 1. Table 1. Standard Frequency Ratios Ratio Name 1:1 Unison 1:2 Octave 1:3 Twelfth 2:3 Fifth 3:4 Fourth 4:5 Major Third 3:5 Major Sixth 5:6 Minor Third 5:8 Minor Sixth 1 These ratios apply both to a fundamental frequency and its overtones, as well as to relationship between separate keys.
  • The Emergence of Low Frequency Active Acoustics As a Critical

    The Emergence of Low Frequency Active Acoustics As a Critical

    Low-Frequency Acoustics as an Antisubmarine Warfare Technology GORDON D. TYLER, JR. THE EMERGENCE OF LOW–FREQUENCY ACTIVE ACOUSTICS AS A CRITICAL ANTISUBMARINE WARFARE TECHNOLOGY For the three decades following World War II, the United States realized unparalleled success in strategic and tactical antisubmarine warfare operations by exploiting the high acoustic source levels of Soviet submarines to achieve long detection ranges. The emergence of the quiet Soviet submarine in the 1980s mandated that new and revolutionary approaches to submarine detection be developed if the United States was to continue to achieve its traditional antisubmarine warfare effectiveness. Since it is immune to sound-quieting efforts, low-frequency active acoustics has been proposed as a replacement for traditional passive acoustic sensor systems. The underlying science and physics behind this technology are currently being investigated as part of an urgent U.S. Navy initiative, but the United States and its NATO allies have already begun development programs for fielding sonars using low-frequency active acoustics. Although these first systems have yet to become operational in deep water, research is also under way to apply this technology to Third World shallow-water areas and to anticipate potential countermeasures that an adversary may develop. HISTORICAL PERSPECTIVE The nature of naval warfare changed dramatically capability of their submarine forces, and both countries following the conclusion of World War II when, in Jan- have come to regard these submarines as principal com- uary 1955, the USS Nautilus sent the message, “Under ponents of their tactical naval forces, as well as their way on nuclear power,” while running submerged from strategic arsenals.
  • Fundamentals of Duct Acoustics

    Fundamentals of Duct Acoustics

    Fundamentals of Duct Acoustics Sjoerd W. Rienstra Technische Universiteit Eindhoven 16 November 2015 Contents 1 Introduction 3 2 General Formulation 4 3 The Equations 8 3.1 AHierarchyofEquations ........................... 8 3.2 BoundaryConditions. Impedance.. 13 3.3 Non-dimensionalisation . 15 4 Uniform Medium, No Mean Flow 16 4.1 Hard-walled Cylindrical Ducts . 16 4.2 RectangularDucts ............................... 21 4.3 SoftWallModes ................................ 21 4.4 AttenuationofSound.............................. 24 5 Uniform Medium with Mean Flow 26 5.1 Hard-walled Cylindrical Ducts . 26 5.2 SoftWallandUniformMeanFlow . 29 6 Source Expansion 32 6.1 ModalAmplitudes ............................... 32 6.2 RotatingFan .................................. 32 6.3 Tyler and Sofrin Rule for Rotor-Stator Interaction . ..... 33 6.4 PointSourceinaLinedFlowDuct . 35 6.5 PointSourceinaDuctWall .......................... 38 7 Reflection and Transmission 40 7.1 A Discontinuity in Diameter . 40 7.2 OpenEndReflection .............................. 43 VKI - 1 - CONTENTS CONTENTS A Appendix 49 A.1 BesselFunctions ................................ 49 A.2 AnImportantComplexSquareRoot . 51 A.3 Myers’EnergyCorollary ............................ 52 VKI - 2 - 1. INTRODUCTION CONTENTS 1 Introduction In a duct of constant cross section, with a medium and boundary conditions independent of the axial position, the wave equation for time-harmonic perturbations may be solved by means of a series expansion in a particular family of self-similar solutions, called modes. They are related to the eigensolutions of a two-dimensional operator, that results from the wave equation, on a cross section of the duct. For the common situation of a uniform medium without flow, this operator is the well-known Laplace operator 2. For a non- uniform medium, and in particular with mean flow, the details become mo∇re complicated, but the concept of duct modes remains by and large the same1.
  • Physics 1240: Sound and Music

    Physics 1240: Sound and Music

    Physics 1240: Sound and Music Today (7/29/19): Percussion: Vibrating Beams *HW 3 due at the front, HW 4 now posted (due next Mon.) Next time: Percussion: Vibrating Membranes Review Types of Instruments (Hornbostel–Sachs classification) • Chordophones: vibrating strings • Aerophones: vibrating columns of air • Idiophones: vibrating the whole instrument • Membranophones: vibrating membrane/skin • Electrophones: vibrating loudspeaker Review Aerophones e.g. flute, e.g. clarinet e.g. saxophone, recorder oboe, bassoon • Free (no standing waves) • Flute-type (edge tones) • Reed-type (vibrating reed/lips) = = = 2 4 1 • How to create waves: Edge tones Bernoulli effect Review • Tone holes, valves: decrease/increase effective length L • Register holes, octave holes: excite 3rd/2nd harmonics • Ear canal: tube closed at one end 1 3 BA Clicker Question 14.1 A 1 m long, homemade PVC pipe flute has a large, open tone hole that is a distance 0.6 m from the source end of the flute. What frequencies are present in the spectrum (in Hz)? A) 286, 572, 857, … B) 143, 286, 429, … C) 143, 429, 715, … D) 286, 857, 1429, … E) 172, 343, 515, … BA Clicker Question 14.1 A 1 m long, homemade PVC pipe flute has a large, open tone hole that is a distance 0.6 m from the source end of the flute. What frequencies are present in the spectrum (in Hz)? A) 286, 572, 857, … B) 143, 286, 429, … • Flute: open-open tube C) 143, 429, 715, … • Tone hole: decreases L D) 286, 857, 1429, … from 1 m to 0.6 m E) 172, 343, 515, … 343 m/s = = 2(0.6 m) = (286 Hz) 2 BA Clicker Question 14.2 An oboe can be modelled as a cone open at one end.
  • Standing Waves Physics Lab I

    Standing Waves Physics Lab I

    Standing Waves Physics Lab I Objective In this series of experiments, the resonance conditions for standing waves on a string will be tested experimentally. Equipment List PASCO SF-9324 Variable Frequency Mechanical Wave Driver, PASCO PI-9587B Digital Frequency Generator, Table Rod, Elastic String, Table Clamp with Pulley, Set of 50 g and 100 g Masses with Mass Holder, Meter Stick. Theoretical Background Consider an elastic string. One end of the string is tied to a rod. The other end is under tension by a hanging mass and pulley arrangement. The string is held taut by the applied force of the hanging mass. Suppose the string is plucked at or near the taut end. The string begins to vibrate. As the string vibrates, a wave travels along the string toward the ¯xed end. Upon arriving at the ¯xed end, the wave is reflected back toward the taut end of the string with the same amount of energy given by the pluck, ideally. Suppose you were to repeatedly pluck the string. The time between each pluck is 1 second and you stop plucking after 10 seconds. The frequency of your pluck is then de¯ned as 1 pluck per every second. Frequency is a measure of the number of repeating cycles or oscillations completed within a de¯nite time frame. Frequency has units of Hertz abbreviated Hz. As you continue to pluck the string you notice that the set of waves travelling back and forth between the taut and ¯xed ends of the string constructively and destructively interact with each other as they propagate along the string.
  • Waves and Music

    Waves and Music

    Team: Waves and Music Part I. Standing Waves Whenever a wave ( sound, heat, light, ...) is confined to a finite region of space (string, pipe, cavity, ... ) , something remarkable happens − the space fills up with a spectrum of vibrating patterns called “standing waves”. Confining a wave “quantizes” the frequency. Standing waves explain the production of sound by musical instruments and the existence of stationary states (energy levels) in atoms and molecules. Standing waves are set up on a guitar string when plucked, on a violin string when bowed, and on a piano string when struck. They are set up in the air inside an organ pipe, a flute, or a saxophone. They are set up on the plastic membrane of a drumhead, the metal disk of a cymbal, and the metal bar of a xylophone. They are set up in the “electron cloud” of an atom. Standing waves are produced when you ring a bell, drop a coin, blow across an empty soda bottle, sing in a shower stall, or splash water in a bathtub. Standing waves exist in your mouth cavity when you speak and in your ear canal when you hear. Electromagnetic standing waves fill a laser cavity and a microwave oven. Quantum-mechanical standing waves fill the space inside atomic systems and nano devices. A. Normal Modes. Harmonic Spectrum. A mass on a spring has one natural frequency at which it freely oscillates up and down. A stretched string with fixed ends can oscillate up and down with a whole spectrum of frequencies and patterns of vibration. Mass on Spring String with Fixed Ends (mass m, spring constant k) (length L, tension F, mass density µ) ___ ___ f = (1/2 π) √k/m f1 = (1/2L) √F/ µ Fundamental nd f2 = 2f 1 2 harmonic rd f3 = 3f 1 3 harmonic th f4 = 4f 1 4 harmonic • • • These special “Modes of Vibration” of a string are called STANDING WAVES or NORMAL MODES .
  • Standing Waves

    Standing Waves

    Chapter 21. Superposition Chapter 21. Superposition The combination of two or more waves is called a superposition of waves. Applications of superposition range from musical instruments to the colors of an oil film to lasers. Chapter Goal: To understand and use the idea of superposition. 1 2 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Principal of superposition Chapter 21. Superposition Topics: • The Principle of Superposition • Standing Waves • Transverse Standing Waves • Standing Sound Waves and Musical Superimposed Superposition Acoustics N • Interference in One Dimension = + + + = • The Mathematics of Interference Dnet D1 D2 ... DN ∑Di i=1 • Interference in Two and Three Dimensions • Beats 3 4 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. When a wave pulse on a string reflects from a hard boundary, how is the reflected pulse related to the incident pulse? A. Shape unchanged, amplitude unchanged Chapter 21. Reading Quizzes B. Shape inverted, amplitude unchanged C. Shape unchanged, amplitude reduced D. Shape inverted, amplitude reduced E. Amplitude unchanged, speed reduced 5 6 Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. When a wave pulse on a string reflects There are some points on a standing from a hard boundary, how is the wave that never move. What are reflected pulse related to the incident these points called? pulse? A. Shape unchanged, amplitude unchanged A. Harmonics B. Shape inverted, amplitude unchanged B.
  • Lab 5A: Mersenne's Laws & Melde's Experiment

    Lab 5A: Mersenne's Laws & Melde's Experiment

    CSUEB Physics 1780 Lab 5a: Mersenne & Melde Page 1 Lab 5a: Mersenne’s Laws & Melde's experiment Introduction Vincenzo Galilei (1520 –1591), the father of Galileo Galilei, was an Italian lutenist, composer, and music theorist. It is reported that he showed that the pitch of a vibrating string was proportional to the square root of its tension. In other words, in order to increase the pitch by an octave (factor of 2 in frequency) it would require the tension to be quadrupled. Marin Mersenne (1588-1648, see picture), often called the “father of acoustics” , around 1630 published a book summarizing the properties of sound, based on the earlier work of Vincenzo and Galileo. He established that: • Frequency is inversely proportional to length of string • Frequency is inversely proportional to the diameter of the string • Frequency is proportional to the root of the tension • Frequency is inversely proportional to the root of the mass (density) of the string. So in summary, if you want a low note, use a fat (massive) long string under low tension. For a high pitch, use a thin short string under high tension. We can summarize all of his results with a single equation showing that the frequency “f” is proportional to: 1 F f ∝ , (1) L µ where “L” is the length of the violin string, “F” is the tension (in Newtons of force) and µ (“mu”) is the mass density of the string (in units of mass per unit length, e.g. kg per meter). In this experiment the string is assumed to be vibrating in its “fundamental” mode, like this, (figure 1).