Page 1 :
Downloaded from https:// www.studiestoday.com, , Chapter, , , , , , SYLLABUS, , (i) Reflection of sound waves; echoes, their use; simple numerical problems on echoes., Scope of syllabus : Production of echoes, condition for formation of echoes; simple numerical problems; use of, echoes by bats, dolphins, fishermen, medical field. SONAR., , (ii) Natural vibrations, damped vibrations, forced vibration and resonance — a special case of forced vibrations., Scope of syllabus : Meaning and simple applications of natural, damped, forced vibrations and resonance., , , , , , (iii) Loudness, pitch and quality of sound., Scope of syllabus : Characteristics of sound; loudness and intensity: subjective and objective nature of these, properties; sound level in dB (as unit only); noise pollution; inter dependence of pitch and frequency, quality, , and waveforms (with examples)., , , , , , , , , , , , 7.1. SOUND WAVES, , In class IX, we have read that sound is, produced when a body vibrates and it reaches us, through the vibrations of the particles of, surrounding medium. Thus sound requires a, medium for its propagation. The vibrations of the, body produce vibrations in the particles of, surrounding medium which travel in form of, waves with a certain speed depending upon the, density and elasticity of the medium. When these, vibrations reach our ear, the sound is heard. Our, ears are sensitive only to a limited range of, frequencies from 20 Hz to 20,000 Hz. This range, of frequency is, therefore, called the range of, audibility. However, the audibility range of a, person decreases as he gets older since the hearing, sensitivity of ears falls for both the low and, high frequencies. The sound of frequency above, 20,000 Hz is called the ultrasonic, while the sound, of frequency below 20 Hz is called the infrasonic., Both the ultrasonic and infrasonic are inaudible to, human beings, but they both travel in a medium, with the speed same as that of the audible sound., , =), , When sound wave travels in a medium, the, maximum displacement of the particle of medium, on either side of its mean position, is called the, amplitude (a) of the wave. The time taken by the, particle of medium to complete its one vibration,, is called the time period (T) of the wave. The, number of vibrations made by the particle of the, medium in one second, is called the frequency (f), of the wave. The frequency of a wave is same as, the frequency of the source producing it. The, distance travelled by a wave in one time period, of vibration of the particle of the medium, is called, the wavelength (A). The distance travelled by the, wave in one second is called the wave velocity (V)., The wave velocity V, frequency f and wavelength 4, are related as :, , eas Til), , , , The time period of wave T and its frequency f, are related as :, , «(7.2), , , , Se ee Ea lo EE See, Downloaded from https:// www.studiestoday.com

Page 2 :
Downloaded from https:// www.studiestoday.com, , , , Note : The frequency (or time period) of wave, depends on the vibrating source producing the, sound, while the velocity of wave and hence, its wavelength depends on the properties of the, medium in which the wave travels., , , , , , , , The sound waves necessarily require a, medium for their propagation. The transfer of, energy by waves is through the vibrations of the, medium particles about their mean positions., When the medium particles vibrate, there is a, change of kinetic energy into the potential energy, and vice versa, so sound waves are also called the, elastic or mechanical waves. The mechanical, waves are of two kinds : (1) longitudinal waves,, and (2) transverse waves. If the vibrations of, medium particles are along the direction of, propagation of the wave, thus forming, compressions and rarefactions in the medium, the, wave is called a longitudinal wave e.g. sound, waves in air, in solid and inside a liquid. The, longitudinal waves can travel in solid, liquid as, well as gas. On the other hand, if the medium, particles vibrate normal to the direction of, propagation of the wave, forming crests and, troughs, the wave is called a transverse wave e.g., sound waves in a solid and on the surface of a, liquid. Transverse waves are formed only in those, media which possess rigidity and that is why they, can travel only in solids and on the surface of a, liquid., , The speed V of a longitudnal wave (i.e., sound), in a gaseous medium of density d at a pressure P, , —_ =|, , where y (the ratio of two specific heats) is 1-4, for air., , Since the density of gas decreases with the, increase in temperature and with the increase in, humidity in it, so the speed of sound increases, with the increase in temperature* and with the, presence of humidity in the gas. However the, , e(7.3), , * For 1°C rise in temperature, the speed of sound in air, increases nearly by 0-61 ms., , , , speed of sound is not affected by the change in, pressure., , The speed V of a transverse wave in a, stretched string depends on the tension T and, mass per unit length m of string. It is given as :, , When a wave travelling in one medium passes, to another medium (i.e., in refraction), the speed,, wavelength and intensity* of the wave will change,, but the frequency of wave will not change. The, direction of travel of wave will also change except, for normal incidence (i.e., for Zi = 0°)., , (7.4), , The sound waves differ from the electromagnetic waves (e.g., y-tays, X-rays, ultraviolet light,, visible light, infrared rays, micro waves, and radio, waves). The electromagnetic waves are formed by, the periodic vibrations of the mutually perpendicular, electric and magnetic fields in a plane normal to the, direction of wave propagation. The electromagnetic, waves are thus the transverse waves, but unlike, sound waves they can travel through vacuum also., The speed of electromagnetic waves is different in, different media and it is maximum (equal to, 3 x 108 ms“) in vacuum (or air). The electromagnetic, waves transfer energy in form of photons., , Distinction between the light and sound waves, , , , * The change in intensity is because of partial reflection at, the boundary surface separating the two media., , 7 Foe eS See, Downloaded from https:// www.studiestoday.com

Page 3 :
Downloaded from https:// www.studiestoday.com, , 7.2 REFLECTION OF SOUND WAVES, , Sound waves, just like any other wave, when, strike a hard surface (or boundary of another, medium), return back in the same medium, obeying the laws of reflection i.e. (i) the angle, of reflection is equal to the angle of incidence,, (ii) the incident ray, reflected ray and normal at, the point of incidence, all lie in one plane. The, return of a sound wave on striking a surface such, as wall, metal sheet, plywood etc. back in the, same medium is called the reflection of sound, wave. The reflection of sound wave does not, require a smooth and shining surface like a, mirror. Sound waves get reflected from any, surface whether smooth or hard. The only, requirement for the reflection of sound wave is, that the size of the reflecting surface must be, bigger than the wavelength of the sound wave., The phenomenon of reflection of sound waves is, utilized in making the megaphone (or speaking, tube), sound board and ear trumpet., , 7.3 ECHO, , Production (or generation) of an echo, , If a person stands at some distance from a wall, (or a hillside) and produces a sharp sound, he hears, two distinct sounds : (i) the original (or direct), , sound which is heard almost instantaneously and, (ii) the sound heard after reflection from the wall, (or hillside) which is called an echo. Thus,, , , , , , Note : The reflected sound if heard along, with the original sound, is not the echo. Only, the sound heard after the original sound has, ceased (i.e., the sound distinctly separate from, the original sound), is called the echo., , , , , , , , Condition for hearing an echo, , An echo is heard only if the distance of the, person producing sound from the rigid obstacle, (or reflector) is long enough to allow the reflected, , =, , sound to reach the person at least 0-1 second, after the original sound is heard. The reason is, that the sensation of sound persists in our ears, for about 0-1 second after the exciting stimulus, ceases to act. Hence to hear the echo distinctly, (separate from the original sound), it must reach, the ears at least 0-1 second after the original, sound., , If d is the distance of the observer from the, obstacle and V is the speed of sound in the, medium, then the total distance travelled by the, sound to reach the obstacle and then to come, back, is 2d. The time taken to hear the echo (or, reflected sound) is, total distance travelled Wd, , speed of sound, , or, , , , By putting t = 0-1 s and V = 340 m s* in air, at ordinary temperature, from eqn. (7.5), we get, 340 x 0-1, , 2., , Thus, to hear an echo distinctly, the reflecting, surface in air should be at a minimum distance, of 17 m from the listener. If the distance is less, than 17 m, the reflected sound will reach the ears, before the original sound dies out and so no echo, will be heard., , Note » (1) If the reflector is at a distance, less than 17 m, the original sound just mixes, up with the reflected sound., , (2) If there are repeated reflections at the, reflecting surface, the sound gets prolonged., This effect is known as reverberation which, can easily be experienced in tombs like Taj, Mahal, Sikandra, etc., , d= = 17m, , , , , , , , , , Thus to hear the echo distinctly, following, three conditions must be satisfied :, (1) The minimum distance between the source, of sound (or observer) and the reflector in, air must be 17 m. It is different in different, medium depending upon the speed of sound, , in that medium. For example, inside sea, , Downloaded from https:// www.studiestoday.com

Page 4 :
Downloaded from https:// www.studiestoday.com, , 1400x0-1, , , , water, V = 1400 ms!, sod =, , = 70 m. i.e., to hear echo distinctly, the, obstacle in sea water should be at a minimum, distance of 70 m from the listener., , The size of the reflector must be large enough, as compared to the wavelength of the sound, ‘wave., , The intensity of sound should be such that, the reflected sound reaching the ear is, sufficiently intense to be audible., , 7.4 DETERMINATION OF SPEED OF, SOUND BY THE METHOD OF ECHO, , The echo method can be used to determine, the speed of sound in air. For this, sound is, produced from a place at a known distance say,, d at least 50 m from the reflecting surface. The, time interval t in which the echo reaches the, place from where the sound was produced, is, noted by a stop watch having the least count, 0-01. s. Then the speed of sound is calculated by, using the following relation :, , (2), , (3), , , , The experiment is repeated several times and, then the average value of speed of sound V is, determined., , 7.5 USE OF ECHOES, , Echoes find their application in sound ranging, and echo depth sounding by using the ultrasonic, waves., , The ultrasonic waves (frequency above, 20 kHz) are used because of the following three, reasons :, , (1), , They can travel undeviated through a long, distance,, , (2), @), , They can be confined to a narrow beam., , They are not easily absorbed in a, medium., , , , Note : Audible sound waves (frequency, 20 Hz to 20 kHz) do not possess the above, properties. However, the ultrasonic waves in a, medium have the same speed as the speed of, audible sound waves in that medium., , , , , , , , (1) Use of echoes by bats, dolphins and, fisherman, , Animals have different range of audible, frequency e.g. bats, dolphins and dogs have a, much higher upper audible limit than the human, beings. Bats can produce and detect the sound of, very high frequency up to about 100 kHz., , Bats fly with speed much lower than the, speed of sound. The sounds produced by the, flying bats get reflected back from an obstacle in, front of it. By hearing the echo, bats come to, know, even in the dark, the location of the, obstacle, so they can fly safely without colliding, with it. This process of detecting obstacle is, called sound ranging., , Dolphins detect their enemy and obstacle by, emitting the ultrasonic waves and hearing their, echo. They use ultrasonic waves for hunting their, prey., , A trawlerman or fisherman sends a pulse of, ultrasonic waves from a source (a very high, frequency vibrator) into the sea and receives the, waves reflected from the shoal of fish in a detector., The total time ¢ of the to and fro journey of the, , wave is recorded. The distance d of fish is then, , calculated by using the relation d = 4 where V, , is nearly 1400 m s” (the speed of ultrasonic waves, in sea water)., , (2) Use of echoes by ‘SONAR’, , The word ‘SONAR’ stands for sound, navigation and ranging. Fig. 7.1 shows the, principle of a sonar in which ultrasonic waves are, sent in all directions from the ship. These waves, are received after reflection from an obstacle such, as the enemy submarine, iceberg, sunken ship, etc., , Downloaded from https:// www.studiestoday.com

Page 5 :
Downloaded from https:// www.studiestoday.com, , , , Fig. 7.1 Principle of sonar, , To find the distance of obstacle from the ship, the time interval t between the instant when, waves (pulse) are sent and the instant when, waves are received, after reflection from the, obstacle is measured. The distance d of the, , obstacle from the source is then d = ye, , where V is the speed of ultrasonic waves in water., The depth of sea can also be found by this, method. The process is then called echo depth, sounding., , , , , and (b) displacement-distance, graph of a wave, travelling in a string with velocity 20 ms“. In, each case, use graph to calculate the frequency, and wavelength of the wave., , , , , x(inm) >, , , , (b), , Fig. 7.2, , Given : Wave velocity V = 20 ms, , (a) From graph in Fig. 7.2(a), the time for, one vibration of wave particle i.e. time period, , T=0-10s, ede De ae, Frequency f= 7 * ios” 10 Hz, From relation V = fA,, Wavelength A = ¥ = * =2m, , (b) From graph in Fig. 7.2(b), length of one wave, ie., wavelength \ = 2 m, From relation V = fA,, , Frequency f = ¥ 25 10 Hz, , , , 1, The diagram below shows (a) displacement-time,, , , , , , Note : (4) In radar (radio detection and, ranging), also the echo method is used to detect, the presence of an obstacle and also to find its, range. A signal of electromagnetic waves (such as, radio waves or micro waves) is sent in space, which after reflection from the object (such as, enemy’s aeroplane) in its path, returns to the radar, itself., , (2) Both in ‘SONAR’ and ‘RADAR’, the, transmitter and the receiver are placed close to, each other. In Fig. 7.1, they are shown separated, just for clarity., , (3) Use of echoes in medical field, , , , , , In medical field, echo method of ultrasonic, waves is used for imaging the human organs, (such as liver, gall bladder, uterus, womb, etc.), This is called ultrasonography. Similarly, echo, cardiography is used to obtain the image of, human heart., , , , 2. A sound produced on the surface of a lake takes, 45 s to reach a boatman. How much time will it, take to reach a diver inside water at the same, distance if speed of sound in water is 4-5 times, the speed of sound in air ?, , Given, V, Vaie = 45, tain = 4:5 8, t, , water * ‘water, , d, , ‘water, , =?, , , , From relation V,,. = eae and V, ster =, , Tain water ~ 7, , or Vii, X tis = Vivater * twater, , , , Voie 1, water = Voag % fair = ag * 45s= 15., , 3. A boy hears an echo of his own voice from a, distant hill after one second. The speed of sound, in air is 350 m s“!, What is the distance of hill, from the boy ?, , Given V=350ms1,t=15., , Let d be the distance of hill from the boy., , Total distance travelled by the sound in going and, then coming back = 2d., , t, , Now speed of sound V = Sotal Revoacs eave, time taken t, se as vxt es et = 175m, , SS eae. 150 ae, Downloaded from https:// www.studiestoday.com