Outdoors propagation free field (point source)

Slides:



Advertisements
Similar presentations
Outdoors propagation free field (point source). The DAlambert equation The equation comes from the combination of the continuty equation for fluid motion.
Advertisements

Angelo Farina Dip. di Ingegneria Industriale - Università di Parma Parco Area delle Scienze 181/A, Parma – Italy
Angelo Farina Dip. di Ingegneria Industriale - Università di Parma Parco Area delle Scienze 181/A, Parma – Italy
Angelo Farina Dip. di Ingegneria Industriale - Università di Parma Parco Area delle Scienze 181/A, Parma – Italy
Angelo Farina Dip. di Ingegneria Industriale - Università di Parma Parco Area delle Scienze 181/A, Parma – Italy
ACOUSTICS part – 3 Sound Engineering Course
Viscosity of Dilute Polymer Solutions
Auditory Neuroscience - Lecture 1 The Nature of Sound auditoryneuroscience.com/lectures.
1 Metamaterials with Negative Parameters Advisor: Prof. Ruey-Beei Wu Student : Hung-Yi Chien 錢鴻億 2010 / 03 / 04.
PH0101 UNIT 2 LECTURE 31 PH0101 Unit 2 Lecture 3  Maxwell’s equations in free space  Plane electromagnetic wave equation  Characteristic impedance 
EEE 498/598 Overview of Electrical Engineering
Physics 151: Lecture 35, Pg 1 Physics 151: Lecture 35 Today’s Agenda l Topics çWaves on a string çSuperposition çPower.
Lecture 24 Physics 2102 Jonathan Dowling EM waves Geometrical optics.
The Propagation of Light
Acoustic Wave Equation. Acoustic Variables Pressure Density – Condensation Velocity (particle) Temperature.
WIRELESS COMMUNICATIONS Assist.Prof.Dr. Nuray At.
Electromagnetic Waves Physics 4 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB.
Chung-Ang University Field & Wave Electromagnetics CH 8. Plane Electromagnetic Waves 8-4 Group Velocity 8-5 Flow of Electromagnetic Power and the Poynting.
Physics 1402: Lecture 26 Today’s Agenda Announcements: Midterm 2: NOT Nov. 6 –About Monday Nov. 16 … Homework 07: due Friday this weekHomework 07: due.
SOUND WAVES AND SOUND FIELDS Acoustics of Concert Halls and Rooms Principles of Sound and Vibration, Chapter 6 Science of Sound, Chapter 6.
Doppler Effect Physics 202 Professor Lee Carkner Lecture 11.
Physics of fusion power Lecture 10 : Running a discharge / diagnostics.
Lectures 11-12: Gravity waves Linear equations Plane waves on deep water Waves at an interface Waves on shallower water.
Doppler Effect Physics 202 Professor Lee Carkner Lecture 11.
Feb. 7, 2011 Plane EM Waves The Radiation Spectrum: Fourier Transforms.
Waves Traveling Waves –Types –Classification –Harmonic Waves –Definitions –Direction of Travel Speed of Waves Energy of a Wave.
Electromagnetic waves Physics 2102 Gabriela González.
Jaypee Institute of Information Technology University, Jaypee Institute of Information Technology University,Noida Department of Physics and materials.
Physics Jeopardy 2nd Trimester Review
1 Sound Propagation in Different Environments What is Sound? Free Field Sound Field Rooms Sound in Motion.
Chapter 14 Sound. Sound waves Sound – longitudinal waves in a substance (air, water, metal, etc.) with frequencies detectable by human ears (between ~
Chapter 17 Sound Waves: part two HW 2 (problems): 17.22, 17.35, 17.48, 17.58, 17.64, 34.4, 34.7, Due Friday, Sept. 11.
Lesson 02 Physical quantities 5 th October 2012Physical quantities1.
Dept. of Mech. Engineering University of Kentucky 1 Wave Motion – Some Basics Sound waves are pressure disturbances in fluids, such as air, caused by vibration,
Ch 2. The Schrödinger Equation (S.E)
Angelo Farina Dip. di Ingegneria Industriale - Università di Parma Parco Area delle Scienze 181/A, Parma – Italy
Physics 1202: Lecture 18 Today’s Agenda Announcements: –Lectures posted on: –HW assignments, etc.
Chapters 16, 17 Waves.
Physics Mechanics Fluid Motion Heat Sound Electricity Magnetism Light.
Geology 5640/6640 Introduction to Seismology 2 Feb 2015 © A.R. Lowry 2015 Read for Wed 4 Feb: S&W (§2.4); Last time: The Wave Equation! The.
Wave Dispersion EM radiation Maxwell’s Equations 1.
5. Interference Interference – combination of waves (an interaction of two or more waves arriving at the same place) Principle of superposition: (a) If.
Physics Mrs. Dimler SOUND.  Every sound wave begins with a vibrating object, such as the vibrating prong of a tuning fork. Tuning fork and air molecules.
Sound Waves  Sound is a longitudinal wave, meaning that the motion of particles is along the direction of propagation.  sound waves are divided into.
What is the absolute power of a sound with an intensity of X dB IL? What is the absolute power corresponding to 20 dB IL? What is the absolute power corresponding.
Chapter 1: Nature of light. waveparticle Wave-particle duality However strange, it correctly describes known phenomena connected with light. E = h.
Real pipes The pressure does not drop to zero right at the open end of a pipe. Because of this, the acoustic length is slightly grater then physical length.
THE RADAR EQUATION ELC 451.
Analytical Methods.
Electromagnetic Waves
Lesson 02 Physical quantities
4.11 Inverse Square Law Point Sources
Properties of sound.
THE RADAR EQUATION ELC 451.
Analyze functions of two variables
Electromagnetic Radiation
Lecture 14 : Electromagnetic Waves
a brief revision of principles and calculations from Building Physics
ACOUSTICS part – 3 Sound Engineering Course
ACOUSTICS part – 4 Sound Engineering Course
Chapter 1: Nature of light
Research Methods in Acoustics Lecture 5: Reflection and Horn Equation
Research Methods in Acoustics Lecture 5: Reflection and Horn Equation
Lecture 12 Chapter 17 Waves II
Reflection and Refraction
5. Interference Interference – combination of waves
Powerpoint Jeopardy! Wave Basics Types of Waves
Electromagnetic radiation; The Solar Spectrum;
Physics 319 Classical Mechanics
Antenna Theory Chapter.4.7.4~4.8.1 Antennas
Presentation transcript:

Outdoors propagation free field (point source)

The D’Alambert equation The equation comes from the combination of the continuty equation for fluid motion and of the 1st Newton equation (f=m·a). In practice we get the Euler’s equation: now we define the potential F of the acoustic field, which is the “common basis” of sound pressure p and particle velocity v: Substituting these identities in Euler’s equation we get: D’Alambert equation Once the equation is solved and F(x, y, z,t) is known, one can compute p and v.

Spherical sound field (pulsating sphere) Let’s consider the sound field being radiated by a pulsating sphere of radius R: This is also called a “monopole” source. We suppose to know the radial velocity of the sphere’s surface, v(R,t): Another related quantity is the “volume velocity” or Source Strenght Q: Where S is the surface’s area (in m2), and hence Q is measured in m3/s

Free field propagation: the spherical wave Let’s consider the sound field being radiated by a pulsating sphere of radius R: v(R,t) = vmax ·ej ej = cos() + j sin() Solving the D’Alambert equation for the outgoing wave (r > R), we get: Finally, thanks to Euler’s formula, we get back to pressure: k = w/c = 2πf/c = 2π/λ wave number

Free field propagation: the spherical wave k = 2p/l

Free field: proximity effect From previous formulas, we see that in the far field (r>>l) we have: But this is not true anymore coming close to the source. When r approaches 0 (or r is smaller than l), p and v tend to: This means that close to the source the particle velocity becomes much larger than the sound pressure.

Free field: proximity effect Low frequency (long length) High frequency (short length) r

Free field: proximity effect The more a microphone is directive (cardioid, hypercardioid) the more it will be sensitive to the partcile velocty (whilst an omnidirectional microphone only senses the sound pressure). So, at low frequency, where it is easy to place the microphone “close” to the source (with reference to l), the signal will be boosted. The singer “eating” the microphone is not just “posing” for the video, he is boosting the low end of the spectrum...

Spherical wave: Impedance If we compute the impedance of the spherical field (Z=p/v) we get: k = 2p/l When r is large, this becomes the same impedance as the plane wave (r ·c), as the imaginary part vanishes. Instead, close to the source (r < l), the impedance modulus tends to zero, and pressure and velocity go to quadrature (90° phase shift). Of consequence, it becomes difficult for a sphere smaller than the wavelength l to radiate a significant amount of energy.

Spherical Wave: Impedance (Magnitude)

Spherical Wave: Impedance (Phase)

Free field: energetic analysis, geometrical divergence The area over which the power is dispersed increases with the square of the distance.

Free field: sound intensity If the source radiates a known power W, we get: Hence, going to dB scale:

Free field: propagation law A spherical wave is propagating in free field conditions if there are no obstacles or surfacecs causing reflections. Free field conditions can be obtained in a lab, inside an anechoic chamber. For a point source at the distance r, the free field law is:  Lp = LI = LW - 20 log r - 11 + 10 log Q (dB)   where LW the power level of the source and Q is the directivity factor. When the distance r is doubled, the value of Lp decreases by 6 dB.

Free field: directivity (1) Many sound sources radiate with different intensity on different directions. Iq I0 Hence we define a direction-dependent “directivity factor” Q as: Q = I / I0 where I è is sound intensity in direction , and I0 is the average sound intensity consedering to average over the whole sphere. From Q we can derive the direcivity index DI, given by: DI = 10 log Q (dB) Q usually depends on frequency, and often increases dramatically with it.

Free Field: directivity (2) Q = 1  Omnidirectional point source Q = 2  Point source over a reflecting plane Q = 4  Point source in a corner Q = 8  Point source in a vertex