DOCSLIB.ORG

Power and Intensity Intensity and Pressure Sound Range of Hearing

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Power and Intensity Intensity and Pressure Sound Range of Hearing Power and Intensity Music 175: Sound Level • pressure Tamara Smyth, [email protected] The waveform shows how sound varies over Department of Music, time. University of California, San Diego (UCSD) • Related to sound pressure are: April 14, 2020 1. sound power emitted by the source: – a fixed quantity, in Watts (W), – analogous to the wattage rating of a light bulb. 2. sound intensity measured a distance from the source: – power per unit area carried by wave (W/m2), – influenced by interference and environment, – analogous to light brightness at different positions in a room. 1 Music 175: Sound Level 2 Intensity and Pressure Sound Range of Hearing • Intensity is the power per unit area, • Amplitude (pressure) range of hearing (humans) Power – Threshold of audibility: 0.00002 N/m2 Intensity = , A – Threshold of feeling (or pain!): 200 N/m2 expressed in Watts/square meter (W/m2). • Sound intensity range (humans) • Sound intensity is −12 2 – I0 = 10 W/m (threshold of audibility) – a measure of the power in a sound that actually – 1 W/m2 (threshold of feeling) contacts an area (e.g. eardrum); • The intensity ratio between the sounds that bring – a quantity influenced by environment pain to our ears and the weakest sounds we can hear surroundings/surfaces and interference from other is more than 1012. sources; • Intensity is related to pressure squared: I = p2/(ρc), where ρ is the density of air (kg/m3), and c is the speed of sound (m/s). Music 175: Sound Level 3 Music 175: Sound Level 4 Linear vs logarithmic scales. Decibels (dB) • Human hearing is better measured logarithmically. • The decibel (dB) is a unit named after • On a linear scale, telecommunications pioneer, Alexander Graham Bell. • – a change between two values is perceived on the To understand decibels DON’T watch. basis of the difference between the values; • The decibel is a logarithmic scale, used to compare – e.g.: a change from 1 to 2 would be perceived as two quantities such as having the same increase as from 4 to 5. – the power gain of an amplifier; • On a logarithmic scale, – the relative power of two sound sources. – a change between two values is perceived on the • A decibel is defined as one tenth of a bel, basis of the ratio of the two values; 1 B = 10 dB. – e.g.: a change from 1 to 2 would be perceived as having the same increase as a change from 4 to 8. (to convert from B to dB, multiply by 10) • Linear: moving one unit to the right adds 1. • To compare quantities A and B: Linear A log = value (B) 10 B −6 −5 −4 −3 −2 −1 0 1 2 43 65 Logarithmic A 0.0001 0.001 0.01 0.1 1 10 100 1000 10,000 10log = value (dB) 10 B • Logarithmic: moving right one unit multiplies by 10. Music 175: Sound Level 5 Music 175: Sound Level 6 Comparing Power and Intensity Power and Intensity Levels • The decibel difference between two power levels ∆L • Decibels are often used as absolute measurements. is defined in terms of their power ratio W2/W1: ∆L = L2 − L1 = 10log W2/W1 dB. • Since power is proportional to intensity, the decibel difference between two levels with intensities I1 and I2 is given by − ∆L = L2 L1 = 10log I2/I1 dB. • There is an implied fixed reference (e.g. the threshold of audibility). • Sound power level of a source: W LW = 10log dB, W0 −12 where W0 = 10 W. • Sound intensity level at a distance from the source I LI = 10log dB, I0 −12 2 where I0 = 10 W/m . Music 175: Sound Level 7 Music 175: Sound Level 8 Sound pressure Level (SPL or Lp) Increasing distance from a source • Recall: intensity is proportional to pressure squared: • Assuming radiation in free space (and equally in all I = p2/(ρc), directions) and a distance r from the source, (where ρc ≈ 400). – intensity decreases by 1/r2 • The sound pressure level Lp (SPL) is equivalent to sound intensity level in dB: Lp = 10log I/I0 2 = 10log p /(ρcI0). • Question: If there is a doubling of distance from • The product of ρ and c is often approximated by 400: the source, by what factor will the intensity change? p2 L = 10log p2/(ρcI ) = 10log • p 0 4 × 10−10 Solution: p 2 – Given an intensity at some initial distance: = 10log 2 × 10−5 P I1 = , p 4πr2 = 20log 2 × 10−5 p – doubling the distance from the source yields, = 20log dB. P P 1 p0 I2 = 2 = 2 2 = 2I1, −5 4π(2r) 2 4πr 2 where p0 =2 × 10 is the threshold of hearing for 2 pressure variations. a change in intensity by a factor of of 1/2 . Music 175: Sound Level 9 Music 175: Sound Level 10 Sound Intensity Level with a Doubling SPL with a Doubling of Distance of Distance • We should obtain the same result for pressure as with • How does the sound level change with a doubling intensity. of distance? • If intensity decreases by 1/r2, then – intensity will drop by a factor of 1/22 or 2−2 and – pressure decreases by 1/r, I − L = 10log 2 2 – (intensity is proportional to pressure squared). I I 0 • With a doubling of distance, pressure will drop by a I − = 10log + 10log(2 2) factor of 1/2 or 2−1, I0 p − I − L = 20log 2 1 = 10log 20 log(2) p p I0 0 p I − = 20log − 20 log(2) = 10log 20(.3) p I0 0 p I − = 20log − 6 dB. = 10log 6 dB. p I0 0 – doubling the distance from a source causes a decrease of 6 dB in the sound level. Music 175: Sound Level 11 Music 175: Sound Level 12 Multiple sources Example SPL Levels • When there are multiple sound sources, the total • The following is taken from Dan Levitin’s, Your Brain power emitted is the sum of the power from each on Music. source. – 0 dB: a mosquito flying in a quiet room, ten feet • By how much would the sound level increase when away from your ears two sources sound simultaneously with equal power? – 20 dB: a recording studio – the sound power level would double, – 35 dB: a typical quiet office with the door closed 2W and computer off LW = 10log – 50 dB: typical conversation W0 W – 75 dB: typical comfortable music listening level = 10log + 10log(2) W0 (headphones) W – 100-105 dB: Classical music concert during loud = 10log +3 dB, W0 passages; the highest level of some portable music players and there would be an increase of 3 dB. – 110 dB: A jackhammer 3 feet away • Similarly, there would be a 3 dB increase in the sound – 120 dB: A jet engine heard on the runway from intensity level measured at some distance away from 300 ft away; typical rock concert the source. – 126-130 dB: Threshold of pain and damage; a • This accounts for most cases; the actual result rock concert by the Who depends on correlation (and interference) of sound – 180 dB: Space shuttle launch sources. Music 175: Sound Level 13 Music 175: Sound Level 14.
Load more

Recommended publications
  • Definition and Measurement of Sound Energy Level of a Transient Sound Source
    J. Acoust. Soc. Jpn. (E) 8, 6 (1987) Definition and measurement of sound energy level of a transient sound source Hideki Tachibana,* Hiroo Yano,* and Koichi Yoshihisa** *Institute of Industrial Science , University of Tokyo, 7-22-1, Roppongi, Minato-ku, Tokyo, 106 Japan **Faculty of Science and Technology, Meijo University, 1-501, Shiogamaguti, Tenpaku-ku, Nagoya, 468 Japan (Received 1 May 1987) Concerning stationary sound sources, sound power level which describes the sound power radiated by a sound source is clearly defined. For its measuring methods, the sound pressure methods using free field, hemi-free field and diffuse field have been established, and they have been standardized in the international and national stan- dards. Further, the method of sound power measurement using the sound intensity technique has become popular. On the other hand, concerning transient sound sources such as impulsive and intermittent sound sources, the way of describing and measuring their acoustic outputs has not been established. In this paper, therefore, "sound energy level" which represents the total sound energy radiated by a single event of a transient sound source is first defined as contrasted with the sound power level. Subsequently, its measuring methods by two kinds of sound pressure method and sound intensity method are investigated theoretically and experimentally on referring to the methods of sound power level measurement. PACS number : 43. 50. Cb, 43. 50. Pn, 43. 50. Yw sources, the way of describing and measuring their 1. INTRODUCTION acoustic outputs has not been established. In noise control problems, it is essential to obtain In this paper, "sound energy level" which repre- the information regarding the noise sources.
    [Show full text]
  • Sound Power Measurement What Is Sound, Sound Pressure and Sound Pressure Level?
    www.dewesoft.com - Copyright © 2000 - 2021 Dewesoft d.o.o., all rights reserved. Sound power measurement What is Sound, Sound Pressure and Sound Pressure Level? Sound is actually a pressure wave - a vibration that propagates as a mechanical wave of pressure and displacement. Sound propagates through compressible media such as air, water, and solids as longitudinal waves and also as transverse waves in solids. The sound waves are generated by a sound source (vibrating diaphragm or a stereo speaker). The sound source creates vibrations in the surrounding medium. As the source continues to vibrate the medium, the vibrations propagate away from the source at the speed of sound and are forming the sound wave. At a fixed distance from the sound source, the pressure, velocity, and displacement of the medium vary in time. Compression Refraction Direction of travel Wavelength, λ Movement of air molecules Sound pressure Sound pressure or acoustic pressure is the local pressure deviation from the ambient (average, or equilibrium) atmospheric pressure, caused by a sound wave. In air the sound pressure can be measured using a microphone, and in water with a hydrophone. The SI unit for sound pressure p is the pascal (symbol: Pa). 1 Sound pressure level Sound pressure level (SPL) or sound level is a logarithmic measure of the effective sound pressure of a sound relative to a reference value. It is measured in decibels (dB) above a standard reference level. The standard reference sound pressure in the air or other gases is 20 µPa, which is usually considered the threshold of human hearing (at 1 kHz).
    [Show full text]
  • 21-4 Sound and Sound Intensity One Way to Produce a Sound Wave in Air Is to Use a Speaker
    Answer to Essential Question 21.3: Doubling the angular frequency, ", causes the frequency to double in part (a). This, in turn, means that that wave speed must double, in part (b). In part (c), the tension is proportional to the square of the speed, so the tension is increased by a factor of 4. In part (e), the maximum transverse speed is proportional to ", so the maximum transverse speed doubles. Finally, in part (f) we get a completely different value, y = – 0.39 cm. 21-4 Sound and Sound Intensity One way to produce a sound wave in air is to use a speaker. The surface of the speaker vibrates back and forth, creating areas of high and low density (corresponding to pressure a little higher than, and a little lower than, standard atmospheric pressure, respectively) in the region of air next to the speaker. These regions of high and low pressure (the sound wave) travel away from the speaker at the speed of sound. The air molecules, on average, just vibrate back and forth as the pressure wave travels through Medium Speed of sound them. In fact, it is through the collisions of air molecules that the sound wave is propagated. Because air molecules are not coupled Air (0°C) 331 m/s together, the sound wave travels through gas at a relatively low Air (20°C) 343 m/s speed (for sound!) of around 340 m/s. As Table 21.1 shows, the Helium 965 m/s speed of sound in air increases with temperature. Water 1400 m/s Steel 5940 m/s For other material, such as liquids or solids, in which there Aluminum 6420 m/s is more coupling between neighboring molecules, vibrations of the Table 21.1: Values of the speed of atoms and molecules (that is, sound waves) generally travel more sound through various media.
    [Show full text]
  • Frequency Response and Bode Plots
    1 Frequency Response and Bode Plots 1.1 Preliminaries The steady-state sinusoidal frequency-response of a circuit is described by the phasor transfer function Hj( ) . A Bode plot is a graph of the magnitude (in dB) or phase of the transfer function versus frequency. Of course we can easily program the transfer function into a computer to make such plots, and for very complicated transfer functions this may be our only recourse. But in many cases the key features of the plot can be quickly sketched by hand using some simple rules that identify the impact of the poles and zeroes in shaping the frequency response. The advantage of this approach is the insight it provides on how the circuit elements influence the frequency response. This is especially important in the design of frequency-selective circuits. We will first consider how to generate Bode plots for simple poles, and then discuss how to handle the general second-order response. Before doing this, however, it may be helpful to review some properties of transfer functions, the decibel scale, and properties of the log function. Poles, Zeroes, and Stability The s-domain transfer function is always a rational polynomial function of the form Ns() smm as12 a s m asa Hs() K K mm12 10 (1.1) nn12 n Ds() s bsnn12 b s bsb 10 As we have seen already, the polynomials in the numerator and denominator are factored to find the poles and zeroes; these are the values of s that make the numerator or denominator zero. If we write the zeroes as zz123,, zetc., and similarly write the poles as pp123,, p , then Hs( ) can be written in factored form as ()()()s zsz sz Hs() K 12 m (1.2) ()()()s psp12 sp n 1 © Bob York 2009 2 Frequency Response and Bode Plots The pole and zero locations can be real or complex.
    [Show full text]
  • Computational Entropy and Information Leakage∗
    Computational Entropy and Information Leakage∗ Benjamin Fuller Leonid Reyzin Boston University fbfuller,[email protected] February 10, 2011 Abstract We investigate how information leakage reduces computational entropy of a random variable X. Recall that HILL and metric computational entropy are parameterized by quality (how distinguishable is X from a variable Z that has true entropy) and quantity (how much true entropy is there in Z). We prove an intuitively natural result: conditioning on an event of probability p reduces the quality of metric entropy by a factor of p and the quantity of metric entropy by log2 1=p (note that this means that the reduction in quantity and quality is the same, because the quantity of entropy is measured on logarithmic scale). Our result improves previous bounds of Dziembowski and Pietrzak (FOCS 2008), where the loss in the quantity of entropy was related to its original quality. The use of metric entropy simplifies the analogous the result of Reingold et. al. (FOCS 2008) for HILL entropy. Further, we simplify dealing with information leakage by investigating conditional metric entropy. We show that, conditioned on leakage of λ bits, metric entropy gets reduced by a factor 2λ in quality and λ in quantity. ∗Most of the results of this paper have been incorporated into [FOR12a] (conference version in [FOR12b]), where they are applied to the problem of building deterministic encryption. This paper contains a more focused exposition of the results on computational entropy, including some results that do not appear in [FOR12a]: namely, Theorem 3.6, Theorem 3.10, proof of Theorem 3.2, and results in Appendix A.
    [Show full text]
  • A Weakly Informative Default Prior Distribution for Logistic and Other
    The Annals of Applied Statistics 2008, Vol. 2, No. 4, 1360–1383 DOI: 10.1214/08-AOAS191 c Institute of Mathematical Statistics, 2008 A WEAKLY INFORMATIVE DEFAULT PRIOR DISTRIBUTION FOR LOGISTIC AND OTHER REGRESSION MODELS By Andrew Gelman, Aleks Jakulin, Maria Grazia Pittau and Yu-Sung Su Columbia University, Columbia University, University of Rome, and City University of New York We propose a new prior distribution for classical (nonhierarchi- cal) logistic regression models, constructed by first scaling all nonbi- nary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-t prior distributions on the coefficients. As a default choice, we recommend the Cauchy distribution with cen- ter 0 and scale 2.5, which in the simplest setting is a longer-tailed version of the distribution attained by assuming one-half additional success and one-half additional failure in a logistic regression. Cross- validation on a corpus of datasets shows the Cauchy class of prior dis- tributions to outperform existing implementations of Gaussian and Laplace priors. We recommend this prior distribution as a default choice for rou- tine applied use. It has the advantage of always giving answers, even when there is complete separation in logistic regression (a common problem, even when the sample size is large and the number of pre- dictors is small), and also automatically applying more shrinkage to higher-order interactions. This can be useful in routine data analy- sis as well as in automated procedures such as chained equations for missing-data imputation. We implement a procedure to fit generalized linear models in R with the Student-t prior distribution by incorporating an approxi- mate EM algorithm into the usual iteratively weighted least squares.
    [Show full text]
  • Sound Intensity and Power
    Sound intensity and power Professor Phil Joseph Departamento de Engenharia Mecânica IMPORTANCE OF SOUND INTENSITY AND SOUND POWER MEASUREMENT . Sound pressure is the quantity usually used to quantify sound fields. However, it is often satisfactory as an measure of source because the pressure propagates as a wave which, due to multi-path interference, may lead to fluctuations with observer position. Sound pressure, unlike measures of sound energy, are not conserved. Performance of noise control systems often specified in terms of energy, e.g., transmission loss, absorption coefficient. INSTANTANEOUS INTENSITY Instantaneous sound intensity I(t) is the rate of acoustic energy flowing through unit area in unit time (Wm-2). If, in a point in space, the acoustic pressure p(t) produces at the same point a particle velocity u(t), the rate at which work is done on the fluid per unit area I(t) at time t is given by It ptut Note that I is a vector quantity in the direction of the particle velocity u ‘PROOF’ The work done on the fluid by Force F acting over a distance d in the direction of the force is Fd The work done per unit area A in unit time T, i.e., the sound intensity, is given by F d I x pu A T EXAMPLES FOR WHICH SOUND INTENSITY AND MEAN SQUARE PRESSURE ARE SIMPLY RELATED 1. Plane progressive waves 2. Far field of a source in free field 3. Hemi-diffuse field However, in general there is no simple relation between intensity and pressure ENERGY CONSERVATION Net rate of change of energy = Rate of energy in – Rate of energy out E I I xy x xy y xy t x t In 3 - dimensions E I I I .It 0 .I x y z t x x x RELATIONSHI[P BETWEEN SOUND IINTENSITY AND SOURCE SOUND POWER Applying Gauss's divergence theorem .A dV A.nˆ dS V S to E .I 0 t gives E W dV I.nˆ dS V t S GENERAL PROPERTIES OF SOUND INTENSITY FIELDS Sound intensity (sometimes called sound power flux density) is a vector quantity acting in the direction of the particle velocity vector u(t).
    [Show full text]
  • 1 1. Data Transformations
    260 Archives ofDisease in Childhood 1993; 69: 260-264 STATISTICS FROM THE INSIDE Arch Dis Child: first published as 10.1136/adc.69.2.260 on 1 August 1993. Downloaded from 1 1. Data transformations M J R Healy Additive and multiplicative effects adding a constant quantity to the correspond- In the statistical analyses for comparing two ing before readings. Exactly the same is true of groups of continuous observations which I the unpaired situation, as when we compare have so far considered, certain assumptions independent samples of treated and control have been made about the data being analysed. patients. Here the assumption is that we can One of these is Normality of distribution; in derive the distribution ofpatient readings from both the paired and the unpaired situation, the that of control readings by shifting the latter mathematical theory underlying the signifi- bodily along the axis, and this again amounts cance probabilities attached to different values to adding a constant amount to each of the of t is based on the assumption that the obser- control variate values (fig 1). vations are drawn from Normal distributions. This is not the only way in which two groups In the unpaired situation, we make the further of readings can be related in practice. Suppose assumption that the distributions in the two I asked you to guess the size of the effect of groups which are being compared have equal some treatment for (say) increasing forced standard deviations - this assumption allows us expiratory volume in one second in asthmatic to simplify the analysis and to gain a certain children.
    [Show full text]
  • The Human Ear  Hearing, Sound Intensity and Loudness Levels
    UIUC Physics 406 Acoustical Physics of Music The Human Ear Hearing, Sound Intensity and Loudness Levels We’ve been discussing the generation of sounds, so now we’ll discuss the perception of sounds. Human Senses: The astounding ~ 4 billion year evolution of living organisms on this planet, from the earliest single-cell life form(s) to the present day, with our current abilities to hear / see / smell / taste / feel / etc. – all are the result of the evolutionary forces of nature associated with “survival of the fittest” – i.e. it is evolutionarily{very} beneficial for us to be able to hear/perceive the natural sounds that do exist in the environment – it helps us to locate/find food/keep from becoming food, etc., just as vision/sight enables us to perceive objects in our 3-D environment, the ability to move /locomote through the environment enhances our ability to find food/keep from becoming food; Our sense of balance, via a stereo-pair (!) of semi-circular canals (= inertial guidance system!) helps us respond to 3-D inertial forces (e.g. gravity) and maintain our balance/avoid injury, etc. Our sense of taste & smell warn us of things that are bad to eat and/or breathe… Human Perception of Sound: * The human ear responds to disturbances/temporal variations in pressure. Amazingly sensitive! It has more than 6 orders of magnitude in dynamic range of pressure sensitivity (12 orders of magnitude in sound intensity, I p2) and 3 orders of magnitude in frequency (20 Hz – 20 KHz)! * Existence of 2 ears (stereo!) greatly enhances 3-D localization of sounds, and also the determination of pitch (i.e.
    [Show full text]
  • C-17Bpages Pdf It
    SPECIFICATION DEFINITIONS FOR LOGARITHMIC AMPLIFIERS This application note is presented to engineers who may use logarithmic amplifiers in a variety of system applica- tions. It is intended to help engineers understand logarithmic amplifiers, how to specify them, and how the loga- rithmic amplifiers perform in a system environment. A similar paper addressing the accuracy and error contributing elements in logarithmic amplifiers will follow this application note. INTRODUCTION The need to process high-density pulses with narrow pulse widths and large amplitude variations necessitates the use of logarithmic amplifiers in modern receiving systems. In general, the purpose of this class of amplifier is to condense a large input dynamic range into a much smaller, manageable one through a logarithmic transfer func- tion. As a result of this transfer function, the output voltage swing of a logarithmic amplifier is proportional to the input signal power range in dB. In most cases, logarithmic amplifiers are used as amplitude detectors. Since output voltage (in mV) is proportion- al to the input signal power (in dB), the amplitude information is displayed in a much more usable format than accomplished by so-called linear detectors. LOGARITHMIC TRANSFER FUNCTION INPUT RF POWER VS. DETECTED OUTPUT VOLTAGE 0V 50 MILLIVOLTS/DIV. 250 MILLIVOLTS/DIV. 0V 50.0 ns/DIV. 50.0 ns/DIV. There are three basic types of logarithmic amplifiers. These are: • Detector Log Video Amplifiers • Successive Detection Logarithmic Amplifiers • True Log Amplifiers DETECTOR LOG VIDEO AMPLIFIER (DLVA) is a type of logarithmic amplifier in which the envelope of the input RF signal is detected with a standard "linear" diode detector.
    [Show full text]
  • Ptechreview-02-1937
    FEBRUÄRY 1937 47 OCTAVES AND DECIBELS By R. VERMEULEN. Summary. With the aid of practical data, the relationships are discussed between the acoustic magnitudes: Pitch' interval and loudness, and the corresponding physical mag- nitudes:' frequency and sound intensity. The object of this article is to emphasise that the logarithmic units, octaves and decibels, should be given preference in acoustics for denoting physical magnitudes. ' Why is a preference shown in acoustics and In music, where without any close insight into the associated subjects for logarithmic scales and are physics of sound the pitch has always been denoted even new units introduced to permit the employment in musical scores by notes, the concept "musical of such scales?' The use of logarithmic scales in or pitch interval" has been introduced to repr,esent acoustics is justified from a consideration of the a specific difference in pitch. The most important characteristics of the human ear, apart from pitch interval is the 0 c t a v e: Two tones which many other advantages offered in both this and are at an interval of an octave have-such a marked other subjects. Reasons for this are that to a natural similarity that musicians have not consid- marked extent' acoustic measurements, and par- ered it necessary to introduce different names for ticularly technical sound measurements, represent them, but have merely distinguished them by attempts to find a substitute for direct judgement means of indices. In addition to the octave, there by means of the ear. An instructive example of are pitch intervals, such as the fifth, fourth and this is offered in the determination of the charac- several others, which are similarly perfectly natural teristics of a loudspeaker, ill which not only must and self-evident, not only because two tones which the reproduced music arid speech be analysed differ from each other by such a pitch interval critically but inter alia the loudness also deter- harmonise with each other, but also, and this is mined, i.e.
    [Show full text]
  • Linear and Logarithmic Scales
    Linear and logarithmic scales. Defining Scale You may have thought of a scale as something to weigh yourself with or the outer layer on the bodies of fish and reptiles. For this lesson, we're using a different definition of a scale. A scale, in this sense, is a leveled range of values/numbers from lowest to highest that measures something at regular intervals. A great example is the classic number line that has numbers lined up at consistent intervals along a line. What Is a Linear Scale? A linear scale is much like the number line described above. They key to this type of scale is that the value between two consecutive points on the line does not change no matter how high or low you are on it. For instance, on the number line, the distance between the numbers 0 and 1 is 1 unit. The same distance of one unit is between the numbers 100 and 101, or -100 and -101. However you look at it, the distance between the points is constant (unchanging) regardless of the location on the line. A great way to visualize this is by looking at one of those old school intro to Geometry or mid- level Algebra examples of how to graph a line. One of the properties of a line is that it is the shortest distance between two points. Another is that it is has a constant slope. Having a constant slope means that the change in x and y from one point to another point on the line doesn't change.
    [Show full text]