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Augustine Griffin
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1 Acoustics of buildings Obtaining right amount of reverberation is the secret of good acoustics Topics: Applied acoustics: Sound transducers and their characteristics. Recording and reproduction of sound. Requisites of good auditorium. Reverberation time, Sabine s formula with derivation hours. Acoustics deals with the production, propagation and reception of sound. Architectural acoustics includes the design and construction of buildings and the design of musical instruments. Reverberation: The sound produced in a hall is undergoing multiple reflections at the walls, ceiling and floor of the hall and lingers on for a longer time. The listener in the hall receives both direct and reflected wave from various surfaces in the hall. As a result the sound persists for some time even after the source stops sounding. Their combined effect decides the quality of the note received. The persistence or prolongation of audile sound even after the source has ceased to produce sound is called reverberation. Reverberation time T: The time interval, after the source of sound is cut off, in which the intensity of a sustained 6 note falls to one millionth ( ) of its original value is called reverberation time. Alternatively, it is the time interval in which the intensity level of sound falls by 6dB. f L is the intensity level of sound at t = and L be the intensity level at t = T, where T is the reverberation time. From the definition of intensity level, L = = log & L log, where is the intensity of least audible sound at Hz, & are intensity of sound at t = and t = T respectively. By definition L L = log log log log = 6dB = = 6 6 log = 6 = = 6 Note: Thus, if intensity of sound falls by times its initial value, the intensity level falls by 6 db. Reverberation time T should be neither too large nor too small. f T is too large the resulting sound persists for a long time and results into confusion due to overlapping of sounds of two syllables uttered in succession. On the other hand, if T is too small; the sound produced ends abruptly and becomes unpleasant to hear. Total absence of reverberation produces an unpleasant effect called dead effect. A room with zero reverberation time is called dead room. Note:. Optimum reverberation time for speech is about second and seconds for music.. The Symphony Hall in Boston which is one of the finest concert halls in the world has reverberation time of.8 seconds when it is fully occupied. 3. T depends on the size of hall, nature and area of reflecting surfaces in the hall. 4. The amount of sound energy absorbed by a surface in a given time to the amount of sound energy falling upon it in the same time is called absorption coefficient of the surface. 5. Absorption coefficient of an open window is unity as it is a perfect absorber. 6. The absorption coefficient of square foot area of an open window is called a sabine. 7. A listener is equivalent to an open window of area 5sq.ft. w.r.t. absorption of sound. Sabine s formula: MBR, VSC, Ballari Acoustics of Building

2 The theory of reverberation was developed by Sabine in 9 and gave an expression for the reverberation time in terms of size of hall, area and absorption coefficient of various surfaces in the hall. The relation for reverberation time is called Sabine s formula. Derivation: The effective absorbing area of the total surface S of absorption coefficient a is given by, A = as f a, a, a3 etc. be the absorption coefficients at each reflection of the surfaces having areas s, s s etc. in a room, then the average value of the absorption coefficient a is given by,, 3 as as + as + a3s3 + a = = s + s + s3 + S Here, S is the sum of all the surface areas in the hall and a is the mean absorption coefficient. f be the instantaneous average intensity (the energy per unit volume) of the hall and d be the fall in intensity due to absorption in a short interval of time dt, then d = andt () Here, n is the number of reflections of sound wave per second. By statistical method, Jaeger showed that sound travels a mean distance of 4V / S between two successive reflections where V is the volume of hall and S is the total area of reflecting surface. f v is the velocity of sound, then time interval between two successive reflections is given by, 4V τ = S v vs Average number of reflections per second, n = = () τ 4V Substituting the value of n from equation () in equation () we get, d vs d vs = a = a dt dt 4V 4V ntegrating within the limits from, intensity at the instant the source is cut off and, intensity in time t, we get, MBR, VSC, Ballari Acoustics of Building d = vs That is, loge = a t 4V vs = exp a t 4V According to the definition of reverberation time time interval in which intensity falls to 6 one millionth of initial value, we get, = vs 6 f t = T is the reverberation time, then exp a t = 4V vs Or, a T = 6ln = V Taking v = 345ms - 3.8V, we get, T = 345aS.65V.65V T = = as as This is the Sabine s formula for the reverberation time in terms of volume of the hall, absorption coefficient and reflecting surface area. t a 4 vs V dt

3 Requisites for good acoustics: To produce sound of optimum quality in a hall, one has to satisfy the following conditions.. Each syllable should be of adequate energy so that sound will be sufficiently loud and intelligible at every part of the hall. This can be done by using loud speakers.. The hall should be designed suitably such that reverberation time must be of optimum value i.e., nearly s for music and nearly s for speech. 3. The sound energy produced should be uniformly distributed throughout the hall. The sound received by the listener should be loud and clear with no effect of echo. This can be achieved by using parabolic reflectors behind the speaker. When a person walks on a hard floor near a row of regularly spaced stairs, each foot step is followed by an echo due to the regular successive reflections which has a musical ring. This is called echelon effect. This effect can be reduced by carpeting the floor and making unequal steps. 4. Sound from outside may enter the hall through the windows and doors. This can be minimized by using double shutters. 5. Curved walls and corners can be avoided to prevent undesirable focusing of sound at some parts and zones of silence. How to obtain optimum reverberation time? The reverberation time depends on the size of hall, surface area and nature of reflecting surfaces inside the hall. The reverberation time can be suitably adjusted by keeping the following points in mind.. Few windows are kept open. Walls and ceilings are covered with perforated asbestos, card boards or felt. 3. Heavy curtains, calendars and charts are hung at various places. 4. Seats are provided with cushions. 5. The reverberation time also depends on the number of audience. Hence a specific number of audiences are required for a hall. Transducers: A device which converts from one form to another form is called a transducer. The device which converts other form of energy in to sound & vice versa is called sound transducers. Generally, transducers are of two types. They are Passive transducers and active/self generating transducers. Passive transducers: t requires an external source of power to function. ts output is a measure of some variations in a physical parameter like pressure, resistance or capacitance. Self generating transducers: t requires no external source of power to function. t gives an external output when stimulated by some physical form of energy. There are two types of sound transducers. They are microphones and loud speakers. Microphone: The microphone is an acoustic transducer which converts sound wave into varying electric current. This current can be amplified and transmitted to distant places by telephone wires or radio. There are different types of microphones as discussed below.. Carbon Microphone: Principle: A solid carbon is a good conductor of electricity but the packed fine granules of carbon offer a considerable resistance depending on how closely granules are packed. By increasing the pressure on the granules, the area of contact between the granules increases the effective resistance decreases and vice versa. Construction: MBR, VSC, Ballari Acoustics of Building 3

4 The carbon granules are packed between a carbon block and a thin highly flexible metal diaphragm. When sound waves strike the diaphragm, the granules are subjected to varying pressure. This results in the variation of electrical resistance in tune with the incident wave. f the microphone is connected in the circuit, the circuit current will vary in accordance with the intensity of incident sound.. Ribbon Microphone: t works on the principle of electro-magnetic induction. A stretched ribbon of duralumin about 6mm wide and 5 to cm long of resistance about ohm is suspended between pole pieces of a permanent magnet, the ribbon is clamped at the ends and is free to move back and forth. When sound is incident on the ribbon, it vibrates in the magnetic field and varying field is induced in it. The frequency of induced emf will respond to the intensity of the incident sound. 3. Crystal Microphone: A crystal subjected to compression or expansion a potential drop is developed across the crystal. This property is known as piezo-electric effect. The magnitude of p.d directly depends on the degree of deformation caused by the incident sound wave. Due to sound wave falling on the piezo-electric crystal, an oscillating voltage is developed across the crystal, which varies in accordance with the sound incident on it. The oscillating electrical signal is amplified and transmitted through telephone wires. 4. Capacitor Microphone: A parallel plate capacitor with one plate is fixed and another is free to move is used as a microphone. When sound falls on a moveable plate, the plate moves back and forth and the capacity of capacitor varies. The resulting variations of the voltage can be amplified to the desired value. 5. Loud speaker: The purpose of a loud speaker is to convert electrical signal into audio signal. t works quite opposite to a microphone. Loud speakers are mainly of two types. They are () fixed coil or moving iron type and () moving coil type. () Fixed coil or Moving ron Loud Speakers: t consists of a permanent horse-shoe magnet with two pole pieces. A steel flexible diaphragm is fixed in the throat of a horn in front of the pole pieces. The fluctuating current corresponding to original sound is passed through the coil wound round the pole pieces. This produces corresponding movements of the diaphragm and the sound is reproduced. n the push pull arrangement, an armature is placed in the annular space between the pair of pole pieces. The diaphragm which consists of waxed paper or parchment, is attached to the armature. The fluctuating current due to a source of sound is amplified and fed to the coil. Vibrations corresponding to the original sound, are set up in the diaphragm, which radiates acoustical energy into the space around the loud speaker. The sound out put is faithful reproduction of the original sound for the range8 to Hz. MBR, VSC, Ballari Acoustics of Building 4

. Moving Coil Loud Speaker: This is essentially an electro-dynamic device to convert electrical energy into sound by causing vibrations of a diaphragm.

5 . Moving Coil Loud Speaker: This is essentially an electro-dynamic device to convert electrical energy into sound by causing vibrations of a diaphragm. A coil of wire C is wound round a former which is rigidly attached to the diaphragm of waxed paper or parchment N in the form of a cone. The former and the diaphragm are suspended and the two are together capable of translator motion along the axis of the former. The coil, called the voice coil, has its axis in the radial field of a permanent magnet M and is capable of translator motion. The amplified current, with fluctuations due to sound, is fed into the coil, which vibrates along with the diaphragm along the axis according to Fleming s left hand rule. The vibrations in amplitude and frequency correspond to the original sound which is thus reproduced. Recording & Reproducing of Sound: t is the process of converting the variations caused by sound into a permanent record which can be manipulated or played back in its original form. The most common method of recording of sound is to use a magnetic medium like a magnetic tape to store music, songs, speech etc. Using a microphone the incoming sound waves are converted into electrical signals. Further these signals are used to magnetize a plastic recording tape coated with a suitable metal oxide. The degree of magnetization varies in accordance with the intensity and frequency of the recording sound. The tape in the form of an audio cassette carries a permanent record of the sounds that are picked up by the microphone. Mechanical recording: n this process, sound waves are used directly to activate a stylus or cutter that engraves a pattern on a disc in accordance with the recording sound. This method was in practice for many years for producing gramophone records. Optical recording: MBR, VSC, Ballari Acoustics of Building 5

6 n this method, the microphone transforms sound waves into electric impulses. These impulses are amplified and made to drive a device that alters the intensity of a light beam. Further, the light beam is focused on a moving film and photographically recorded track is obtained on the film. To reproduce the sound a source of light is focused on the film with a photoelectric cell behind the film. As the film passes between the source of light and the photocell a varying electric signal is generated. This signal can be amplified and fed to the loud speaker for the conversion into sound. Sound on a film: There are two techniques used in recording of sound on a film.. Optical method: n this method a transparent line is recorded along one side of the film. The width of the strip varies in accordance with the frequency of the sound. A bright source of light is provided by an exciter lamp. The light is focused on the transparent line by a lens. The emerging light from the film shines on a photocell. The photocell converts the incident light into electric current. The strength of current determines the amount of light received by the photocell. The changing amount of light emerging from the transparent strip results in a variable current. This current is boosted by a preamplifier and fed to amplifier which distributes the signal to the speaker.. Magnetic method: t has two advantages. t is stereo where as the optical method is mono. The magnetic method has better sound quality. The disadvantages of this method are the sound recording must be done after the movie is filmed and it is a costlier. t does not last long and is more easily damaged. $ $ $ MBR, VSC, Ballari Acoustics of Building 6

ONLINE TUTORIALS. Log on using your username & password. (same as your ) Choose a category from menu. (ie: audio)

ONLINE TUTORIALS. Log on using your username & password. (same as your ) Choose a category from menu. (ie: audio) ONLINE TUTORIALS Go to http://uacbt.arizona.edu Log on using your username & password. (same as your email) Choose a category from menu. (ie: audio) Choose what application. Choose which tutorial movie.