DOCSLIB.ORG

EE1.El3 (EEE1023): Electronics III Acoustics Lecture 19 Musical

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
EE1.El3 (EEE1023): Electronics III Acoustics Lecture 19 Musical EE1.el3 (EEE1023): Electronics III Acoustics lecture 19 Musical acoustics Dr Philip Jackson www.ee.surrey.ac.uk/Teaching/Courses/ee1.el3 Musical acoustics Objectives: • identify the acoustic source and filter elements • relate instrument properties to acoustic theory • calculate resonance frequencies for instruments Topics: • string • percussion • woodwind • brass • voice S.1 Preparation for musical acoustics • For one instrument from each class, identify what cre- ates a sound source, and a resonator that enhances it? { voice { woodwind { brass { percussion { string S.2 Types of musical instrument • string & percussion • woodwind & brass • voice S.3 Acoustic model of musical instruments Source: • mechanical vibration Time domain: • coupled vibration s(n) = h(m) ∗ x(n) aero-acoustic • 1 = X h(m) x(n−m) Filter: m=0 • sound box Frequency domain: • pipe resonance • instrument's timbre S(!) = H(!) X(!) sound x(n) acoustical s(n) output generation filter, h(m) sound pressure S.4 Acoustic filters Mechanical resonance • String (guitar, violin, piano) • Bar (xylophone, triangle) • Membrane (tympani, drums) • Shell (bell, cymbal) Acoustic resonance • Open & closed pipes • Low-frequency resonance S.5 Low-frequency resonance When the wavelength is very large compared to the size of an object, acoustic variables are effectively uniform over it at any time instant: it acts as a lumped acoustic element. S x A low-frequency resonator δx can be formed from a chamber with a hole or VV+ δV a neck, e.g., a bottle. P0 P0 + δp The gas density varies inversely with the volume δρ δV Sδx = − = − (1) ρ0 V V inducing an adiabatic change in pressure 2 2δρ δp = c δρ = ρ0c (2) ρ0 which combine to give 2Sδx δp = −ρ0c (3) V S.6 The Helmholtz resonator The force from pressure difference across the air in the neck opposes an inertial force due to its acceleration: 2 2S x Fpressure = Sp = −ρ0c (4) V Finertia = mx¨ = ρ0SLx¨ (5) Ignoring any losses, we obtain the SHM equation of motion: c2S Lx¨ + x = 0 (6) V 2 2 with !H = c S=LV and Helmholtz resonance frequency: s c S f = (7) S H 2π LV L V S.7 Acoustic resonators Open pipes LO Half-closed pipes LS Low-frequencyS Helmholtz L V S.8 Acoustic filters Waveguide geometry can be used to enhance or attenuate given frequencies: Low pass (expansion) High pass (contraction) Band stop (anti-resonator) S.9 Acoustic sources Energy: Mechanism: • plucking • emission of vibration into sound • bowing • mechanical and acoustic resonance • striking • aeroacoustic flow oscillation • blowing S.10 Strings & percussion: source Mechanical vibration of strings, bars, membranes, shells T y + dy dx dx ds θ dy y dx T x x + dx From previous analysis, we obtained the 1D wave equation: @2y @2y − v2 = 0 (8) @t2 @x2 for vibration on a string, where the wave velocity is q v = T/ρL and general solutions have the form: x x y(t; x) = y(+) t − + y(−) t + (9) v v for any arbitrary waveforms, y(+)(·) and y(−)(·) S.11 Modes of a string We obtain (complex) solutions for sinusoidal waves x x (+) j! t− (−) j! t+ y(t; x) = y e ( v ) + y e ( v ) (10) Boundary conditions, y0 = yL = 0, give resonant mode shapes j!t nv y (x; t) = An sin (2πf(n)x) e , where f(n) = n 2L S.12 Modes of a membrane Solving boundary conditions for 2D standing waves gives: Modes of a shell S.13 Strings & percussion: filter Resonance of the sound box to provide instrument's timbre: guitar, violin, piano S.14 Mode shapes of a guitar's sound box S.15 Woodwind & brass: coupled source & filter Oscillation of the reed/lips matches a resonance frequency of the pipe, which determines the pitch of a note: clarinet, oboe, saxophone, trumpet, horn, trombone, tuba S.16 Aero-acoustic source Oscillation of the air matches a pipe resonance frequency: whistle, pipe, flute, organ S.17 Organ pipes S.18 Organ pipe's source and its boundary conditions Flow-coupled source Pulse reflections S.19 Resonances of organ pipe's filter n c f(n) = 2LO (2m − 1)c f(m) = 4LS S.20 Voice as an instrument Vocal source x(n) and filter h(m): s(n) = h(m) ∗ x(n) S(!) = H(!) X(!) voice output vocal−tract filter source S.21 Musical acoustics • Acoustical techniques for making music: { sound generation, resonance and filtering • Musical instruments: { string & percussion { woodwind & brass { voice • Musical sound sources: { mechanical vibration: string, bar, membrane, shell { coupled vibration: reed, lips { aero-acoustic: overblow, whistle • Musical use of resonance: { sound box amplification from cavity { pitch selection using pipe resonance { resonance to provide instrument's timbre S.22 Preparation for sound localisation • What acoustic factors give us the ability to localise sounds with our two ears? { identify and describe at least two acoustic cues that we use, based on the sound pressure signals arriving at the ears S.23 Appendix Trigonometric identities for mode shape derivation ejx = cos x + j sin x (11) ejx + e−jx cos x = = cosh jx (12) 2 ejx − e−jx sin x = = −j sinh jx (13) 2j S.24.
Load more

Recommended publications
  • Acoustic Resonance Lab 1 Introduction 2 Sound Generation
    Summer Music Technology 2013 Acoustic Resonance Lab 1 Introduction This activity introduces several concepts that are fundamental to understanding how sound is produced in musical instruments. We'll be measuring audio produced from acoustic tubes. General Notes • Work in groups of 2 or 3 • Divide up the tasks amongst your group members so everyone contributes Equipment Check Make sure you have the following: • (2) iPads • (1) Microphone • (1) Tape Measure • (1) Adjustable PVC tube with speaker • (1) Amplifier • (1) RCA to 1/8" audio cable • (1) iRig Pre-Amp • (2) Pieces of speaker wire • (1) XLR cable • (1) Pair of Alligator clips 2 Sound Generation Setup We will use one iPad to generate tones that will play through our tube. However, the iPad can't provide enough power to drive the speaker, so we need to connect it to an amplifier. From here on, we'll refer to this iPad as the Synthesizer. 1. Plug the Amplifier’s power cord into an outlet. DO NOT TURN IT ON. 2. Plug one end of the 1/8" audio cable to the iPad's headphone output jack. Plug the other end into the Amplifier’s Input jack. 3. Attach the alligator clips to the speaker wires on the Amplifier’s Output jack. Attach the other end of the clips to the speaker terminals (the speaker should be mounted to the tube). MET-lab 1 Drexel University Summer Music Technology 2013 3 Sound Analysis Setup In order to measure the audio, we need to record audio from a microphone. The other iPad will be used to record sound.
    [Show full text]
  • Nuclear Acoustic Resonance Investigations of the Longitudinal and Transverse Electron-Lattice Interaction in Transition Metals and Alloys V
    NUCLEAR ACOUSTIC RESONANCE INVESTIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERACTION IN TRANSITION METALS AND ALLOYS V. Müller, G. Schanz, E.-J. Unterhorst, D. Maurer To cite this version: V. Müller, G. Schanz, E.-J. Unterhorst, D. Maurer. NUCLEAR ACOUSTIC RESONANCE INVES- TIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERAC- TION IN TRANSITION METALS AND ALLOYS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-389-C6-391. 10.1051/jphyscol:19816113. jpa-00221175 HAL Id: jpa-00221175 https://hal.archives-ouvertes.fr/jpa-00221175 Submitted on 1 Jan 1981 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. JOURNAL DE PHYSIQUE CoZZoque C6, suppZe'ment au no 22, Tome 42, de'cembre 1981 page C6-389 NUCLEAR ACOUSTIC RESONANCE INVESTIGATIONS OF THE LONGITUDINAL AND TRANSVERSE ELECTRON-LATTICE INTERACTION IN TRANSITION METALS AND ALLOYS V. Miiller, G. Schanz, E.-J. Unterhorst and D. Maurer &eie Universit8G Berlin, Fachbereich Physik, Kiinigin-Luise-Str.28-30, 0-1000 Berlin 33, Gemany Abstract.- In metals the conduction electrons contribute significantly to the acoustic-wave-induced electric-field-gradient-tensor (DEFG) at the nuclear positions. Since nuclear electric quadrupole coupling to the DEFG is sensi- tive to acoustic shear modes only, nuclear acoustic resonance (NAR) is a par- ticularly useful tool in studying the coup1 ing of electrons to shear modes without being affected by volume dilatations.
    [Show full text]
  • THE SPECIAL RELATIONSHIP BETWEEN SOUND and LIGHT, with IMPLICATIONS for SOUND and LIGHT THERAPY John Stuart Reid ABSTRACT
    Theoretical THE SPECIAL RELATIONSHIP BETWEEN SOUND AND LIGHT, WITH IMPLICATIONS FOR SOUND AND LIGHT THERAPY John Stuart Reid ABSTRACT In this paper we explore the nature of sound and light and the special relationship that exists between these two seemingly unrelated forms of energy. The terms 'sound waves' and 'electromagnetic waves' are examined. These commonly used expressions, it is held, misrepresent science and may have delayed new discoveries. A hypothetical model is proposed for the mechanism that creaIL'S electromagnetism. named "Sonic Propagation of Electromagnetic Energy Components" (SPEEC). The SPEEC hypothesis states that all sounds have an electromagnetic component and that all electromagnetism is created as a consequence of sound. SPEEC also predicts that the electromagnetism created by sound propagation through air will be modulated by the same sound periodicities that created the electromagnetism. The implications for SPEEC are discussed within the context of therapeutic sound and light. KEYWORDS: Sound, Light, SPEEC, Sound and Light Therapy Subtle Energies &- Energy Medicine • Volume 17 • Number 3 • Page 215 THE NATURE OF SOUND ound traveling through air may be defined as the transfer of periodic vibrations between colliding atoms or molecules. This energetic S phenomenon typically expands away from the epicenter of the sound event as a bubble-shaped emanation. As the sound bubble rapidly increases in diameter its surface is in a state of radial oscillation. These periodic movements follow the same expansions and contractions as the air bubble surrounding the initiating sound event. DE IUPlIUlIEPIESEITInU IF ..... mBIY II m DE TEll '..... "'EI' II lIED, WIIIH DE FAlSE 111101111 DAT ..... IUYEIJ AS I lAVE.
    [Show full text]
  • 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.
    [Show full text]
  • Acoustic Resonance Between Ground and Thermosphere
    Data Science Journal, Volume 8, 30 March 2009 ACOUSTIC RESONANCE BETWEEN GROUND AND THERMOSPHERE 1 1 2 3 1 1 4 Matsumura, M., * Iyemori, T., Tanaka, Y., Han, D., Nose, M., Utsugi, M., Oshiman, N., 5 1 6 Shinagawa, H., Odagi, Y. and Tabata, Y. *1 Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan E-mail: [email protected] 2 Faculty of Engineering, Setsunan University, Neyagawa 572-8508, Japan 3 Polar Research Institute of China, Pudong, Jinqiao Road 451, Shanghai 200136, China 4 Disaster Prevention Research Institute, Kyoto University, Uji 611-0011, Japan 5 National Institute of Information and Communications Technology, Koganei 184-8795, Japan 6Research Institute for Sustainable Humanosphere, Kyoto University, Uji 611-0011, Japan ABSTRACT Ultra-low frequency acoustic waves called "acoustic gravity waves" or "infrasounds" are theoretically expected to resonate between the ground and the thermosphere. This resonance is a very important phenomenon causing the coupling of the solid Earth, neutral atmosphere, and ionospheric plasma. This acoustic resonance, however, has not been confirmed by direct observations. In this study, atmospheric perturbations on the ground and ionospheric disturbances were observed and compared with each other to confirm the existence of resonance. Atmospheric perturbations were observed with a barometer, and ionospheric disturbances were observed using the HF Doppler method. An end point of resonance is in the ionosphere, where conductivity is high and the dynamo effect occurs. Thus, geomagnetic observation is also useful, so the geomagnetic data were compared with other data. Power spectral density was calculated and averaged for each month. Peaks appeared at the theoretically expected resonance frequencies in the pressure and HF Doppler data.
    [Show full text]
  • Sine Waves and Simple Acoustic Phenomena in Experimental Music - with Special Reference to the Work of La Monte Young and Alvin Lucier
    Sine Waves and Simple Acoustic Phenomena in Experimental Music - with Special Reference to the Work of La Monte Young and Alvin Lucier Peter John Blamey Doctor of Philosophy University of Western Sydney 2008 Acknowledgements I would like to thank my principal supervisor Dr Chris Fleming for his generosity, guidance, good humour and invaluable assistance in researching and writing this thesis (and also for his willingness to participate in productive digressions on just about any subject). I would also like to thank the other members of my supervisory panel - Dr Caleb Kelly and Professor Julian Knowles - for all of their encouragement and advice. Statement of Authentication The work presented in this thesis is, to the best of my knowledge and belief, original except as acknowledged in the text. I hereby declare that I have not submitted this material, either in full or in part, for a degree at this or any other institution. .......................................................... (Signature) Table of Contents Abstract..................................................................................................................iii Introduction: Simple sounds, simple shapes, complex notions.............................1 Signs of sines....................................................................................................................4 Acoustics, aesthetics, and transduction........................................................................6 The acoustic and the auditory......................................................................................10
    [Show full text]
  • Analytical Explorations of Spectral Mixed Music
    Musical Engagements with Technology: Analytical Explorations of Spectral Mixed Music Lesley Friesen Schulich School of Music, Department of Music Research McGill University, Montréal August 2015 A thesis submitted to McGill University in partial fulfillment of the requirements of the degree of Master of Arts. © Lesley Friesen, 2015. 2 Table of Contents Abstract ....................................................................................................................................... 4 Résumé ........................................................................................................................................ 5 Acknowledgements ..................................................................................................................... 6 1. Introduction and Background 1.1 Introduction ........................................................................................................................... 7 1.2 The Dualism of Mixed Music – At the Intersection of Two Music Traditions .................. 11 1.3 Classifying Relationships in Mixed Works ........................................................................ 15 1.4 Spectralism and Ambiguity................................................................................................. 18 1.5 “Music for Human Beings:” Psychoacoustics and Auditory Scene Analysis .................... 22 2. Mapping out Methodologies 2.1 Geography of Analysis ......................................................................................................
    [Show full text]
  • Acoustic Resonance Rejection Via Voltage Modulation Method for Hps Lamps
    ACOUSTIC RESONANCE REJECTION VIA VOLTAGE MODULATION METHOD FOR HPS LAMPS L.M.F. MORAIS, P.F. DONOSO-GARCIA, S.I.SELEME JR, P. C. CORTIZO, F.N.A. SILVA Universidade Federal de Minas Gerais Departamento de Engenharia Eletronicaˆ 31270-901 Belo Horizonte, MG - BRASIL Emails: [email protected], [email protected], [email protected], porfi[email protected], [email protected] Abstract— A voltage modulation method in order to prevent the resonance evolutes with some drastic consequence [7], acoustic resonance (AR)inHPS lamps is presented. Two voltage [8], [9]; PWM modulation techniques via inverter are proposed. The first 4) Using square current waves in low frequency, this method one injects harmonic components in the lamp voltage reference. The second one consist of high frequency voltage modulated by avoids the AR because the instantaneous power of a a low frequency waveform. These techniques allow the control square wave is theoretically constant [10], [11], [12]; of crest factor other than rejecting the AR. 5) Driving the lamp with DC current also avoids acoustic Keywords - Acoustic resonance avoidance, HPS lamps, har- resonance [13]; monics injection, PWM, modulation low frequency. 6) Using square current waves of high frequency also pre- vents the acoustic resonance but this approach implies I. INTRODUCTION in high levels of electromagnetic interference (EMI), specially radio frequency emitted by the discharge itself; HPS High pressure sodium ( ) lamps present some nice 7) A way of reducing the interference levels of the approach characteristics, such as high light efficiency, long lifetime 6) above and yet, preventing the occurrence of acoustic (around 24,000 hours) and pleasant colors, which justify its resonance is to superimpose some harmonics (the third large scale use in public lighting.
    [Show full text]
  • High-Overtone Bulk Acoustic Resonator
    Chapter 13 High-Overtone Bulk Acoustic Resonator T. Baron, E. Lebrasseur, F. Bassignot, G. Martin, V. Pétrini and S. Ballandras Additional information is available at the end of the chapter http://dx.doi.org/10.5772/56175 1. Introduction Piezoelectricity has been used for the development of numerous time&frequency passive devices [1]. Among all these, radio-frequency devices based on surface acoustic waves (SAW) or bulk acoustic waves (BAW) have received a very large interest for bandpass filter and frequency source applications. Billions of these components are spread each year around the world due to their specific functionalities and the maturity of their related technologies [2]. The demand for highly coupled high quality acoustic wave devices has generated a strong innovative activity, yielding the investigation of new device structures. A lot of work has been achieved exploiting thin piezoelectric films for the excitation and detection of BAW to develop low loss RF filters [3]. However, problems still exist for selecting the layer orientation to favor specific mode polarization and select propagation characteristics (velocity, coupling, temperature sensitivity, etc.). Moreover, for given applications, deposited films reveal incapable to reach the characteristics of monolithic substrates [4]. For practical implementation, BAW is applied for standard low frequency (5 to 10MHz) shear wave resonators on Quartz for instance. SAW, Film Bulk Acoustic Resonator (FBAR) and High overtone Bulk Acoustic Resonator (HBAR) devices are applied for standard radio- frequency ranges and more particularly in S band (2 to 4GHz). HBAR have been particularly developed along different approaches to take advantage of their extremely high quality factor and very compact structure.
    [Show full text]
  • Vocal Tract Resonances in Singing: Strategies Used by Sopranos, Altos, Tenors, and Baritones Nathalie Henrich Bernardoni, John Smith, Joe Wolfe
    Vocal tract resonances in singing: Strategies used by sopranos, altos, tenors, and baritones Nathalie Henrich Bernardoni, John Smith, Joe Wolfe To cite this version: Nathalie Henrich Bernardoni, John Smith, Joe Wolfe. Vocal tract resonances in singing: Strategies used by sopranos, altos, tenors, and baritones. Journal of the Acoustical Society of America, Acoustical Society of America, 2011, 129 (2), pp.1024-1035. 10.1121/1.3518766. hal-00569451 HAL Id: hal-00569451 https://hal.archives-ouvertes.fr/hal-00569451 Submitted on 25 Aug 2011 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Vocal tract resonances in singing: Strategies used by sopranos, altos, tenors, and baritones Nathalie Henrich Department of Speech and Cognition, GIPSA-lab (UMR5216: CNRS, INPG, University Stendhal, UJF), Grenoble, France John Smith and Joe Wolfe School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia (Received 13 July 2010; revised 21 October 2010; accepted 27 October 2010) The first two vocal tract resonances (R1 and R2) of 22 classically trained sopranos, altos, tenors, and baritones were measured while they sang four different vowels over their normal pitch range. The resonances of the tract and the harmonics of the voice were measured simultaneously by injecting a broadband acoustic current into the tract at their mouth.
    [Show full text]
  • Systems of Acoustic Resonance at Ancient Sites and Related Brain Activity Preliminary Results of the Research
    Systems of acoustic resonance at ancient sites and related brain activity Preliminary results of the research Prof.agg. Paolo Debertolis Prof.ass. Giancarlo Tirelli Dr. Fabrizio Monti Department of Medical Sciences Department of Medical Science Head of Clinical Neurophysiological University of Trieste (Italy) Head and Neck Department Unity Chair of Dental Archaeology University of Trieste (Italy) Department of Neurology, Project SB Research Group (*) Director of Otorhinolaryngology University Hospital of Trieste, Italy Clinic (*) Note . SB Research Group (SBRG) is an international and Introduction interdisciplinary team of researchers (from Italy, Croatia, Finland and United Kingdom) researching the archaeo-acoustics of ancient Archaeoacoustics is an emerging archaeological discipline sites and temples in Europe ( www.sbresearchgoup.eu ). that involves the study of ancient site using an interdisciplinary approach. In previous studies carried out, Abstract – Research was carried out in collaboration with researchers found some Neolithic temples or hypogea had the Head and Neck Department and the Clinical an interesting and particular resonance. SBRG group also found this to be the case in research carried out in Neurophysiological Unit at the University of Trieste [2,3,4,5,6] (Italy) to assess the effects of resonance phenomena on the Europe ; was it possible some temples were built not human body. We worked with volunteers who underwent only as sacred places but also for acoustical resonance examination by EEG while listening to tones between 90Hz effects? and 120Hz, similar to the resonant sounds found at some Such studies were first carried out by Princeton Engineering Anomalies Research Group (PEAR), University of Neolithic structures in Europe (England, Ireland, Italy, [8] Malta).
    [Show full text]
  • Simulation and Inversion of Harmonic Infrasound from Open-Vent Volcanoes Using an Efficient Quasi-1D Crater Model
    Simulation and inversion of harmonic infrasound from open-vent volcanoes using an efficient quasi-1D crater model Leighton M. Watsona, Eric M. Dunhama,b, Jeffrey B. Johnsonc aDepartment of Geophysics, Stanford University, Stanford, California, United States bInstitute of Computational and Mathematical Engineering, Stanford University, Stanford, California, United States cDepartment of Geosciences, Boise State University, Boise, Idaho, United States Abstract Volcanic activity excites low frequency acoustic waves, termed infrasound, in the atmosphere. Infrasound observa- tions can be used to provide constraints on eruption properties, such as crater geometry and volume flux. At open-vent volcanoes, such as Erebus (Antarctica) and Villarrica (Chile), the infrasound signal is modulated by the crater prop- erties. Eruptive activity at the bottom of the crater, such as unsteady degassing or explosions, can excite the air mass within the crater into resonance leading to infrasound generation with signals possessing clear spectral peaks, termed harmonics. Therefore, the effect of the crater on the infrasound signal, or crater acoustic response, must be accounted for when inverting harmonic infrasound observations for eruption properties at open-vent volcanoes. Here we de- velop a linearized model of quasi-one-dimensional (1D) wave propagation inside volcanic crater coupled with 3D axisymmetric radiation into the atmosphere from the crater, with waves generated by a volumetric flow rate source at the bottom of the crater. We perform simulations for a range of volcanic crater geometries, temperature profiles, gas compositions, and source descriptions to explore the influence of these properties on the infrasound signal. The ob- served infrasound signal depends on the flow rate source-time function, but interference of up- and down-going waves within the crater selectively amplifies the signal at the resonant frequencies of the crater.
    [Show full text]