Lesson Propagation of sound Sound fields Spherical, cylindrical and perpendicular wave fronts.

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1 Lesson 13 Basic Concepts in Architectural Acoustics 13.1 Introduction The nature of sound Sound waves Frequency range of sound The audible range of sound Properties of sound Wavelength of sound Period and frequency of sound The inverse square law of sound Speed, frequency and wavelength of sound Speed of sound and the medium of transmission Sound pressure Sound pressure and frequency Pitch Propagation of sound Sound fields Spherical, cylindrical and perpendicular wave fronts Other factors Sound power and sound intensity Measurement of sound Sound power Decrease of sound intensity with distance from source Relationship between sound intensity and sound pressure Effect of barriers on sound Reflection and refraction of sound Transmission and absorption of sound Diffusion of sound Masking and diffraction of sound Sound insulation Reverberation Echoes. Tests and Exercises. References Introduction This lecture covers basic architectural acoustics including the properties and nature of sound, the terms used to describe sound waves; and the relationship between sound pressure, sound intensity and sound power. Sound is measured on the decibel or phon scale. Audible sounds range from the threshold of audibility to the threshold of pain. Basic concepts in acoustics include absorption, diffraction, echo, insulation, masking, reflection, refraction, reverberation and transmission of sound. 1

2 13.2. The Nature of Sound Acoustics is the science of sound. Noise is any unwanted sound, and is a subjective concept. Acoustics covers two areas, those of room acoustics and control of noise. Noise is defined as unwanted or damaging sound, that is, sound which interferes with what people are trying to do, or sound which has an adverse effect on health or safety. To be able to deal with the problems of noise we must first have an understanding of basic architectural acoustics - the nature of sound and its physical properties Sound waves An understanding of the nature of sound waves is essential to discussion on acoustics. Sound waves are longitudinal waves originating from a source and conveyed by a medium. Sound is a disturbance, or wave, which moves through a physical medium (such as air, water or metal) from a source to cause the sensation of hearing in animals. Sound is the sensation of the medium acting on the ear. The source can be a vibrating solid body such as the string of a guitar or the membrane of a drum, but it can also be a vibrating gaseous medium, such as air in a whistle. The medium may be either a fluid or a solid. For example, consider a vibrating tuning fork as the source and the air as the medium. As a prong of the fork moves outward, air molecules in contact with it are also moved and cause a region of raised pressure (called a compression). When the prong moves inward, the air pressure on its outer edge is lowered (called a rarefaction), and the air molecules move back. This motion is passed on to adjacent molecules and in this manner a sound wave propagates and energy is transferred, even though each molecule only oscillates around a central position. This process can be visualized if you can get hold of a coiled spring. Vibrate one end and watch the coils compress and stretch out. A sound wave is characterized by its velocity, frequency, wavelength and amplitude. The frequency is the number of waves per unit time while the velocity is the product of the wavelength and the frequency. See figure x. The 2 Figure x: Compression and rarefaction of sound by a vibrating tuning fork. Figure x: Visualization of sound rarefaction and compression in a coiled spring. Figure x: Changes in sound pressure over time. Figure x: Sound pressure superimposed on atmospheric pressure.

3 amplitude indicates the intensity of the sound. The power of the source is measured in watts (W) while the intensity is measured in watts per square metre (W/m2) Frequency range of sound Sounds over a large range of frequencies can be produced. The lowest note on the piano is 28 Hz, the highest is 4186 Hz, whilst Middle C is 262 Hz. Sound with a frequency below 20 Hz is called infrasound. Sound with a frequency above Hz is called ultrasound The Audible range of sound The average human ear can perceive sound of frequencies between 20 and 16,000Hz. This range varies with individuals, age and other subjective factors. The range audible to young people with undamaged hearing is about 20Hz to 20,000Hz and for adults 20 to 16,000Hz. Some people can hear sounds of lower frequencies. The range is normally reduced with advancement in age. Some blind people are credited with hearing sounds inaudible to the majority of people, even to the extent of using this ability for echo-location. The limit of hearing is also affected by the intensity of the sound. The lower limit is the threshold of audibility and it has a standard value of 1 pw/m2 (1 picowatt per metre square). This is equivalent to W/m2. The upper limit is the threshold of pain and it has a standard value of l W/m2. As the names suggest, sounds below the lower limit are inaudible while sound above the upper limit may cause pain and even damage the ear. The audible range of sound is shown in figure x. The human ear is less sensitive to sounds of higher intensities and this is important in preventing damage. The sound level scale is the logarithm of the ratio of measured sound intensity to the intensity at the threshold of audibility. This scale is also known as the decibel (db) scale Different combinations of frequencies and levels of sound produce the same sensation of loudness. This is due to the variation of the sensitivity of the ear with frequency. Thus loudness cannot be directly measured by instruments. Loudness is determined by referring to the loudness or phon scale which shows Violin Figure x: Sound wave illustration. Figure x: Audible range of sound. Figure x: Audible range of sound. 3

4 sounds of various levels and frequencies which are perceived as of the same loudness. See figure x. The negative effect of noise on man increases with the noise level. The degree of disturbance caused depends on individuals and subjective factors. Urban dwellers are more tolerant of noise than rural dwellers while noise levels acceptable in the day may be quite disturbing at night. Sudden noises are also more disturbing than monotonous noises. The effect of noise on any average human being may be psychological and physiological and it ranges from annoyance to permanent and immediate loss of hearing as shown in table Table 13.1: Psychological and physiological effects of sounds. Noise level Possible psychological and physiological effects. 65 dba Annoyance, mental and physical fatigue. 90dBA Very long exposure may cause permanent hearing loss. Short exposure may cause temporary 100dBA damage, long exposure may cause permanent damage. 120 dba Pain. 150dBA Immediate loss of hearing. Figure x: Equal loudness contours. Figure x: The characteristics of machine noise. Figure x: Relationship between sound pressure and sound frequency in a pure tone. 4

5 13.3 Properties of sound Wavelength of sound Wavelength is the distance between two successive pressure peaks. Its symbol is and it is measured in units of meters (m) Period and Frequency Period is the time taken for one vibration cycle. Its symbol is T and its unit is seconds (s). Frequency is the number of vibration cycles per 1 f second. TIts symbol is f and it is measured in units called hertz (Hz) (named after Heinrich Hertz the German physicist who studied electromagnetic waves). Frequency and period are related by f 1 T For example, a sound with a period of 0.002s has a frequency of 500 Hz The Inverse Square Law of Sound States that the intensity of sound in a free field is indirectly proportional to the square of the distance from the source. This infers a decrease in the intensity of sound the farther the observer is from the source. See figure x Speed, Frequency and Wavelength of Sound Wave velocity is the speed with which sound travels through the medium. Its symbol is c and its unit meters per second (m/s). It is related to the frequency (f) and wavelength ( ) by: c=f So, if you know the speed and frequency of a sound, you can work out the wavelength by: Figure x: The inverse square law of sound. Figure x: Variation of speed of sound with medium of transmission. The cowboy will hear the train noise via the rails before he hears it through the air. Source: US Department of Labour (1980). c f Similarly, for frequency, f c 5

6 Speed of Sound and the Medium of Transmission The speed of sound depends on the medium (its elasticity and density) and its temperature. In air the relationship is: c = K where K is the absolute temperature: ie K = temperature in C So at 21 C the speed of sound in air is: = = 344 m/s. In water the speed of sound is 1470 m/s and in steel, 5050 m/s Sound Pressure The pressure changes produced by a sound wave are known as the sound pressure. Compared with atmospheric pressure (about pascals) they are very small (between 20 micropascals and 200 pascals) and are superimposed on it. The changes in sound pressure at a point over time can be depicted on a graph. See figure x. Figure x: Intensity illustration Sound Pressure and Frequency A sound may contain waves of only one frequency, in which case it is called a pure tone. Noise is made up of waves of many different frequencies and magnitudes superimposed on one another. Sound Pressure is the force per unit area and gives the magnitude of the wave. Its symbol is p and its unit is pascal (Pa). (Named after Blaise Pascal , French physicist and philosopher who was first to measure altitude by barometric pressure.) A quantity known as the root-mean-square pressure, prms, is often used in acoustic measurements, to overcome the problem of the average pressure being zero Pitch Pitch is the property of sound that perceived as highness and lowness. In music, it is the highness or lowness of a musical tone as determined by the rapidity of the vibrations producing it. Changes in pitch are caused by differences in the frequency at which a sound wave vibrates, measured in cycles per second (cps). A high 6 Figure x: High and low frequency illustration. Figure x: Amplitude illustration. Figure x: Pitch illustration.

7 pitch sound corresponds to a high frequency and a low pitch sound corresponds to a low frequency. Amazingly, many people, especially those who have been musically trained, are capable of detecting a difference in frequency between two separate sounds which is as little as 2 Hz. When two sounds with a frequency difference of greater than 7 Hz are played simultaneously, most people are capable of detecting the presence of a complex wave pattern resulting from the interference and superposition of the two sound waves. Certain sound waves when played simultaneously will produce a particularly pleasant sensation when heard, are said to be consonant. The ability of humans to perceive pitch is associated with the frequency of the sound wave which impinges upon the ear. Because sound waves are longitudinal waves which produce high- and low-pressure disturbances of the particles of a medium at a given frequency, the ear has an ability to detect such frequencies and associate them with the pitch of the sound. But pitch is not the only property of a sound wave detectable by the human ear. Pitch determines the placement of a note on a musical scale, corresponding to a standard, specified frequency and intensity. It is often used to tune both instruments and voices to one another. Some people have the inborn ability, known as perfect pitch, to recognize or sing a given note without reference to any other pitch Propagation of Sound Sound Fields Inside a room, sound waves from a source will reflect from the walls, ceiling, floor and other objects in the room. Close to a source like a machine, the direct sound dominates and the sound pressure may vary significantly with just small changes in position. This area is called the near field and its extent is about twice the machine's dimension or one wavelength of the sound. The area beyond the near field is called the far field. This is made up of two sections - the free field where the direct sound still dominates and the sound pressure level decreases 6 db for each doubling of distance, and the reverberant field where the reflected sound adds to the direct Figure x: The near field and far field of sound. Source: National Institute for Occupational Health and Safety (1988). Figure x: Decrease in sound intensity for an omnidirectional point source. 7

8 sound and the decrease per doubling of distance will be less than 6 db Spherical, cylindrical and perpendicular wave fronts. Spherical Wave Fronts When sound spreads out from a point source in a free space the wave fronts are spherical and the sound pressure level will decrease 6 db for each doubling of distance. Cylindrical Wave Fronts When sound spreads out from a line source (such as a road with constant traffic or a pipe carrying fluid), the wave fronts are cylindrical and the sound pressure level will decrease 3 db for each doubling of distance. Perpendicular Wave Fronts When sound spreads out from a plane source (such as close to a large, vibrating panel or sound traveling down a duct) the wave fronts are perpendicular to the direction of propagation and the sound pressure level does not decrease with distance Other Factors The above relationships hold true only in ideal conditions. In reality the decrease in sound levels will be affected by: absorption by the air and moisture in it; wind and temperature gradients; absorption of the ground; and reflection and absorption by obstacles in the path. The first three of these are significant over long distances and are important in the study of environmental noise annoyance. However, they do not play a significant role in occupational noise exposures and so will not be considered further here. Figure x: Decrease in sound pressure level for an omnidirectional point source. Figure x: Decrease in sound intensity for a point source with doubling of distance. Figure x: Decrease in sound intensity for a line source with doubling of distance Sound Power & Sound Intensity Measurement of Sound. The strength of or loudness perception of sound depends on the energy content and determines the pressure variation produced. The amplitude of the sound wave have the maximum 8 Figure x: Decrease in sound pressure level for a line source.

9 displacement of each air particle a generated from stronger sounds. The strength of a sound can be determined by measuring some aspect of its energy and pressure. Even though sound does not involve large amount of energy and its effects depends upon high sensitivity of the human hearing Sound Power. A sound source can be characterized by the sound power which it emits to the surrounding medium. This is a fundamental property of the source and is not affected by the surroundings, such as reflecting surfaces. Hence it is often specified by machine manufacturers so different sources can be compared. Sound power is the energy emitted by a sound source per unit time. The symbol for sound power is W and its unit is the watt. (Named after the Scottish mechanical engineer James Watt, , of steam engine fame.) A source that emits power equally in all directions is called an omnidirectional source. Any other source is called a directional source Decrease of Sound Intensity with Distance from Source. Sound intensity, at a point in the surrounding medium, is the power passing through a unit area. Its symbol is I and its unit, watts/m2. Where: W is the sound power in watts and S is the surface area in m2 For an omnidirectional point source, the sound wave spreads out from the source in all directions. The sound power, W, of the source is hence spread over the surface of a sphere. SoS=4 r2 And I I W 4 r W S where r is the radius of the sphere (ie the distance from source) in meters. 2 Figure x: Perpendicular wave fronts. As the distance from the source increases, the sound intensity decreases according to the "inverse square law". In terms of decibels this means that when r doubles there will be a drop of 6 db in sound level Relationship between Sound Intensity and Sound Pressure. As most measurements of sound are in terms of sound pressure (p), it is useful to know the relationship between sound intensity and sound pressure: Where: I is the sound intensity in watts/m2 p is the sound pressure in Pa is the density of medium in kg/m3 C is the speed of sound in m/s For air at 21 C, 2 p I c = 1.2 kg/m3 and following the equation above: c = 344 m/s Therefore, I = = p2 Strictly speaking, this equation is for plane waves (ie waves propagating with parallel wavefronts). However, away from a point source, the spherical waves approximate plane waves Effect of barriers on sound Reflection and refraction of sound. When a sound wave encounters an obstacle such as a barrier or wall, its propagation will be affected in one of three ways - reflection, diffraction and refraction. Reflection occurs when an obstacle's 9

10 dimensions are larger than the wavelength of the sound. In this case the sound ray behaves like a light ray and, for an obstacle with a flat surface, the reflected ray will leave the surface at the same angle as the incident ray approached it, so that the angle of incidence is equal to the angle of reflection. Refraction occurs when a sound ray enters a different medium at an angle. Because of the differing speed of travel of the sound wave in the two media, the sound ray will bend. This can be an important consideration in outdoor sound propagation over long distances. When weather conditions produce a temperature inversion, sound rays originally propagating upwards can be bent back to the ground Transmission and Absorption of Sound. Some of the energy of sound waves is transmitted to solid barriers in the path of the sound. This energy causes vibration of the molecules of the barrier which may then re-emit the sound. Sound transmitted in this way is referred to as structure-borne sound. When it is generated by mechanical means it is referred to as impact sound. Sound transmitted through the air is known as airborne sound. Not all sound incident on a barrier is transmitted. Some is absorbed by the barrier while the rest is reflected. Thus sound may be: - transmitted (t) - absorbed (a) - reflected (r) The absorption co-efficient is an indication of the sound that is not reflected and is thus an indication of both the sound absorbed and transmitted. Absorption ( a ) is the product of the absorption coefficient and the area of a given surface. It is measured in the `open window unit' which is equivalent to the absorption of a square meter opening with zero reflectance. When a sound wave strikes an obstacle, part of it is reflected, part is absorbed within the obstacle and part is transmitted through to become a sound wave in air again on the other side. The 10 Figure x: Reflection of sound. Figure x: Refraction of sound with no temperature inversion. Figure x: Refraction of sound with temperature inversion.

11 obstacle's ability to block transmission of sound depends on its structure and is indicated by its transmission loss rating. Stiff, heavy materials stop a lot of sound by reflecting most of it and hence have a high transmission loss. Examples are sheet metal, timber, bricks and concrete. Soft, porous materials are not good at blocking the transmission of sound. The fraction of sound energy which is absorbed by an obstacle is called its absorption coefficient. Soft, porous material such as open cell foams and fibrous materials are good absorbers of sound and have an absorption coefficient close to 1. Hard, nonporous materials are poor absorbers and have coefficients as low as Diffusion of sound. Diffusion is the scattering or random redistribution of a sound wave from a surface. It occurs when the surface depths of hard-surface materials are comparable to the wavelength of the sound. Diffusion does not break up or absorb sound. However, the direction of the incident sound wave is changed as it strikes a sounddiffusing material. When satisfactory diffusion has been achieved in a room, listeners or users of the room will have the sensation of sound coming from all directions at equal levels Masking and Diffraction of Sound The shadow effect of screens or barriers in the path of sound differs in accordance with the frequency and wavelength of the sound and the dimensions of the barrier. This effect disappears when the wavelength of the sound wave is more than the dimension of the barrier in a direction perpendicular to the sound path. At high frequencies the acoustic shadow is very distinct but it is somewhat reduced at low frequencies by diffraction. See figure x. Diffraction occurs when an obstacle's dimensions are of the same order or less than the wavelength of the sound. In this case the edge of the obstacle acts like a source of sound itself and the sound ray appears to bend around the edge. This limits the effectiveness of barriers Sound Insulation. Sound insulation is the reduction of sound transmission of airborne sounds through walls, floors and partitions. Figure x: Transmission and absorption of sound. Figure x: Diffraction of sound. Figure x: Acoustic shadow at high frequencies. Appropriate sound insulation is achieved by using elements with an adequate transmission co-efficient or sound reduction index. The transmission co-efficient is a decimal fraction expressing the proportion of sound energy transmitted. The sound reduction index or transmission loss defines the reduction effect of an element and is expressed in decibels. 11

12 Reverberation. When a sound is produced in a room sound waves spread from the source in spherical waves. When these waves strike a surface, some will be reflected. This reflected sound continues spreading until it strikes another surface which reflects it again and so on. This continues even after the actual source has ceased producing sound. However, some of the sound is absorbed at every reflection and the sound energy reduces progressively until the sound becomes inaudible. Reverberation is the persistence of sound in an enclosed space as a result of repeated reflection or scattering, after the sound source has stopped. Reverberation time is the number of seconds required for the energy of the reflected sound in a room to diminish to onemillionth of the original energy it had. It can also be defined as the number of seconds required for the sound pressure level to diminish to 60 decibels below its initial value Echoes. An echo is a distinct repetition of the direct sound. This effect may be observed by making a short sound, such as a sharp clap, in a large room. Tests and Exercises. 1. Define architectural acoustics and its relevance to the architect. 2. Explain which physical parameter of the wave is affected and how, by each of the following processes: A. Reverberation B. Absorption 3. Write concisely on: A. Masking of sound B. Sound absorbers C. Reverberation time. 4. Write a short essay on "Acoustics of Buildings". 5. What is noise? Discuss the harmful effect of noise on man. 6. Define the following terms: A. Echo b. Reverberation C. Reverberation time D. Wave frequency E. Wave velocity 7. Briefly explain the meaning of the following: A. Inverse square law of sound B. Structure-borne sound C. Transmission loss D. Threshold of audibility. 8. What is meant by reverberation and reverberation time? On what factors does the duration of reverberation depend? Why does the magnitude of reverberation time affect the suitability of a hall for speech and music? References. Callender, J.H. (1974). Time-Saver Standards for Architectural Design Data. McGraw-Hill Book Company. Evans, M. (1980). Housing, Climate and Comfort. The Architectural Press, London. Givoni, B. (1976). Man, Climate And Architecture. Second Edition. Applied Science Publishers Ltd., London. Koenigsberger, O.H., Ingersoll, T.G., Mayhew, A. and Szokolay, S.V. (1974). Manual of Tropical Housing And Building, Part I, Climatic Design. Longman, London. Markus, T.A. and Morris, E.N. (1980). Buildings, Climate and Energy. Pitman International, London. National Universities Commission (1977). Standards Guide for Universities. National Universities Commission, Lagos. Olgyay, V. (1963). Design With Climate - Bioclimatic Approach To Architectural Regionalism. Princeton University Press, Princeton, New Jersey. United Nations (1971). Design of Low Cost Housing and Community Facilities, Volume I, Climate and House Design. Department of Economic and Social Affairs, New York. 12