The Sound of Music the Sound of Many Musical Instruments Is the Result of Vibrations Resonating Within a Column of Air
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A Comparison of Viola Strings with Harmonic Frequency Analysis
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Student Research, Creative Activity, and Performance - School of Music Music, School of 5-2011 A Comparison of Viola Strings with Harmonic Frequency Analysis Jonathan Paul Crosmer University of Nebraska-Lincoln, [email protected] Follow this and additional works at: https://digitalcommons.unl.edu/musicstudent Part of the Music Commons Crosmer, Jonathan Paul, "A Comparison of Viola Strings with Harmonic Frequency Analysis" (2011). Student Research, Creative Activity, and Performance - School of Music. 33. https://digitalcommons.unl.edu/musicstudent/33 This Article is brought to you for free and open access by the Music, School of at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Student Research, Creative Activity, and Performance - School of Music by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. A COMPARISON OF VIOLA STRINGS WITH HARMONIC FREQUENCY ANALYSIS by Jonathan P. Crosmer A DOCTORAL DOCUMENT Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Musical Arts Major: Music Under the Supervision of Professor Clark E. Potter Lincoln, Nebraska May, 2011 A COMPARISON OF VIOLA STRINGS WITH HARMONIC FREQUENCY ANALYSIS Jonathan P. Crosmer, D.M.A. University of Nebraska, 2011 Adviser: Clark E. Potter Many brands of viola strings are available today. Different materials used result in varying timbres. This study compares 12 popular brands of strings. Each set of strings was tested and recorded on four violas. We allowed two weeks after installation for each string set to settle, and we were careful to control as many factors as possible in the recording process. -
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. -
Musical Acoustics - Wikipedia, the Free Encyclopedia 11/07/13 17:28 Musical Acoustics from Wikipedia, the Free Encyclopedia
Musical acoustics - Wikipedia, the free encyclopedia 11/07/13 17:28 Musical acoustics From Wikipedia, the free encyclopedia Musical acoustics or music acoustics is the branch of acoustics concerned with researching and describing the physics of music – how sounds employed as music work. Examples of areas of study are the function of musical instruments, the human voice (the physics of speech and singing), computer analysis of melody, and in the clinical use of music in music therapy. Contents 1 Methods and fields of study 2 Physical aspects 3 Subjective aspects 4 Pitch ranges of musical instruments 5 Harmonics, partials, and overtones 6 Harmonics and non-linearities 7 Harmony 8 Scales 9 See also 10 External links Methods and fields of study Frequency range of music Frequency analysis Computer analysis of musical structure Synthesis of musical sounds Music cognition, based on physics (also known as psychoacoustics) Physical aspects Whenever two different pitches are played at the same time, their sound waves interact with each other – the highs and lows in the air pressure reinforce each other to produce a different sound wave. As a result, any given sound wave which is more complicated than a sine wave can be modelled by many different sine waves of the appropriate frequencies and amplitudes (a frequency spectrum). In humans the hearing apparatus (composed of the ears and brain) can usually isolate these tones and hear them distinctly. When two or more tones are played at once, a variation of air pressure at the ear "contains" the pitches of each, and the ear and/or brain isolate and decode them into distinct tones. -
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
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 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. -
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. -
Ch 12: Sound Medium Vs Velocity
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. -
Musical Acoustics Timbre / Tone Quality I
Musical Acoustics Lecture 13 Timbre / Tone quality I Musical Acoustics, C. Bertulani 1 Waves: review distance x (m) At a given time t: y = A sin(2πx/λ) A time t (s) -A At a given position x: y = A sin(2πt/T) Musical Acoustics, C. Bertulani 2 Perfect Tuning Fork: Pure Tone • As the tuning fork vibrates, a succession of compressions and rarefactions spread out from the fork • A harmonic (sinusoidal) curve can be used to represent the longitudinal wave • Crests correspond to compressions and troughs to rarefactions • only one single harmonic (pure tone) is needed to describe the wave Musical Acoustics, C. Bertulani 3 Phase δ $ x ' % x ( y = Asin& 2π ) y = Asin' 2π + δ* % λ( & λ ) Musical Acoustics, C. Bertulani 4 € € Adding waves: Beats Superposition of 2 waves with slightly different frequency The amplitude changes as a function of time, so the intensity of sound changes as a function of time. The beat frequency (number of intensity maxima/minima per second): fbeat = |fa-fb| Musical Acoustics, C. Bertulani 5 The perceived frequency is the average of the two frequencies: f + f f = 1 2 perceived 2 The beat frequency (rate of the throbbing) is the difference€ of the two frequencies: fbeats = f1 − f 2 € Musical Acoustics, C. Bertulani 6 Factors Affecting Timbre 1. Amplitudes of harmonics 2. Transients (A sudden and brief fluctuation in a sound. The sound of a crack on a record, for example.) 3. Inharmonicities 4. Formants 5. Vibrato 6. Chorus Effect Two or more sounds are said to be in unison when they are at the same pitch, although often an OCTAVE may exist between them. -
Harmonic Template Neurons in Primate Auditory Cortex Underlying Complex Sound Processing
Harmonic template neurons in primate auditory cortex underlying complex sound processing Lei Fenga,1 and Xiaoqin Wanga,2 aLaboratory of Auditory Neurophysiology, Department of Biomedical Engineering, Johns Hopkins University School of Medicine, Baltimore, MD 21205 Edited by Dale Purves, Duke University, Durham, NC, and approved December 7, 2016 (received for review May 10, 2016) Harmonicity is a fundamental element of music, speech, and animal role in harmonic integration in processing complex sounds. Pa- vocalizations. How the auditory system extracts harmonic structures tients with unilateral temporal lobe excision showed poorer embedded in complex sounds and uses them to form a coherent performance in a missing fundamental pitch perception task than unitary entity is not fully understood. Despite the prevalence of normal listeners but performed as normal in the task when the f0 sounds rich in harmonic structures in our everyday hearing envi- was presented (21). Auditory cortex lesions could impair complex ronment, it has remained largely unknown what neural mechanisms sound discrimination, such as animal vocalizations, and vowel-like are used by the primate auditory cortex to extract these biologically sounds without affecting responses to relative simple stimuli, like important acoustic structures. In this study, we discovered a unique pure tones (22–24). class of harmonic template neurons in the core region of auditory Primate auditory cortex is subdivided into a “core” region, cortex of a highly vocal New World primate, the common marmoset consisting of A1 and the neighboring primary-like rostral (R) and (Callithrix jacchus), across the entire hearing frequency range. Mar- rostral–temporal areas, surrounded by a belt region, which contains mosets have a rich vocal repertoire and a similar hearing range to multiple distinct secondary fields (Fig. -
Voltage and Frequency Dependency
System Operability Framework Voltage and Frequency Dependency The demand and generation we see on the electricity network has been changing in recent years and is set to continue to change into the future. One of the affects of this change is how frequency and voltage disturbances interact with each other. They will interact more in the future, driving a dynamic voltage requirement. Executive Summary changes in the future, so will the combined frequency and voltage effect change. Frequency and voltage are usually considered and assessed independently in the design and operation of Figure 1 summarises the decline in synchronous electrical networks. However, they are intrinsically linked. generation likely to be seen in the next 10 years, according This investigation seeks to understand this relationship, to current trends. Our Future Energy Scenarios (FES)[1] how it is changing over time and how it may behave in details this further. different regions of Great Britain (GB). This study has found that to support frequency and All faults on our system, such as a line or generator voltage recovery, additional dynamic voltage support will tripping, will have a combined frequency and voltage be required to replace that which is currently provided by effect. In the future, with the reduction in synchronous synchronous generation. Distributed energy recourses generation, combined events will be more significant and (DER) could also provide this in the future, in addition to will need to be considered. other technologies. Each area studied in this assessment has a unique set of National Grid has recently published a road map for results. -
Lecture 38 Quantum Theory of Light
Lecture 38 Quantum Theory of Light 38.1 Quantum Theory of Light 38.1.1 Historical Background Quantum theory is a major intellectual achievement of the twentieth century, even though we are still discovering new knowledge in it. Several major experimental findings led to the revelation of quantum theory or quantum mechanics of nature. In nature, we know that many things are not infinitely divisible. Matter is not infinitely divisible as vindicated by the atomic theory of John Dalton (1766-1844) [221]. So fluid is not infinitely divisible: as when water is divided into smaller pieces, we will eventually arrive at water molecule, H2O, which is the fundamental building block of water. In turns out that electromagnetic energy is not infinitely divisible either. The electromag- netic radiation out of a heated cavity would obey a very different spectrum if electromagnetic energy is infinitely divisible. In order to fit experimental observation of radiation from a heated electromagnetic cavity, Max Planck (1900s) [222] proposed that electromagnetic en- ergy comes in packets or is quantized. Each packet of energy or a quantum of energy E is associated with the frequency of electromagnetic wave, namely E = ~! = ~2πf = hf (38.1.1) where ~ is now known as the Planck constant and ~ = h=2π = 6:626 × 10−34 J·s (Joule- second). Since ~ is very small, this packet of energy is very small unless ! is large. So it is no surprise that the quantization of electromagnetic field is first associated with light, a very high frequency electromagnetic radiation. A red-light photon at a wavelength of 700 −19 nm corresponds to an energy of approximately 2 eV ≈ 3 × 10 J ≈ 75 kBT , where kBT denotes the thermal energy.