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Shri Shivaji Shikshan Prasarak Mandal , Barshi, , KARMVEER SCHOLARS’ ACADEMY, St, , Std-XI, , Physics I, , Sound, Wave – An oscillatory disturbance traveling, through medium with out change of form is, called wave., Eq. – (Rope waves) water waves, sound waves,, Radio waves, electromagnetic waves, 1. Mechanical waves – Waves which required, material medium for the propagation are called, meehanical waves., Eg- sound waves, waves on water surface, 2. Electromagnetic waves - Waves which donot, required material medium for the propagation, are called electromagnetic waves. They can, travel through vacuum, Eg – Light waves, Radio waves, 3. Matter waves: There is always a wave, associated with any object if it is in motion., Such waves are matter waves. These are studied, in quantum mechanics., Proparties of the medium 1. The medium sould be elastic, so that it, can regain it’s original condition when, the wave has passed through it., 2. The medium should possess inertia. So, that it can store energy & transfer it in the, form of wave., 3. The frictional resistance of the medium, should be small so that loss of energy, when waves pass through it is minimum, Mechanical waves can be classified in to, two types, 1. Transvers waves The waves in which particles of the, medium vibrate in a direction perpendicular to, , KSA/ XII/ RBG/ 2021/Sound, , Notes, , the direction of propagation of waves are called, transvers waves, Longitudinal waves The waves in which particles of the, medium vibrate in a direction parallel to the, direction of propagation of waves are called, longitudinal waves., Wave motion – The motion of the oscillatory, disturbance through the medium is called waves, motion, Que - Explain wave motion is doubly periodic, phenomenon –, When waves travel through the medium., at any given point of the medium, the form of the, waves repeats from time to time. Which shows, that wave motion is periodic in time, At any instant the form of waves repeats, at equal distance which shows that wave motion, is periodic in space., Thus wave motion is doubly periodic, phenomenon. i.e. periodic in space & periodic, in time., Terms related to wave motion –, 1. Amplitude (a) – The maximum, displacement of the particle form its mean, position is called the amplitude of, oscillation., S.I. unit is meter, 2. Period (T): Time required to complete, one vibration by a particle of the medium, is the period T of the wave. It is measured, in seconds., 3. Frequency (n) – The number of, oscillations performed by the particle in, one sce. is called frequency of oscillation, , 1

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n=, , 1, S.I. unit is per sec or Hz, T, , 4. Wavelength () The distance, between two consecutive particles of the, medium which are in the same phase (i.e., same state of vibration and they are about, to move in the same direction) of, vibration is called wavelength., S.I. unit of wavelength is m, 5. Velocity (V) of wave - The distance, traveled by the waves in one second is, called the velocity of the waves., Phase –, Phase and phase difference:, Fig. 8.1 (a): Displacement as a function of, distance along the wave., , Fig. 8.1 (b): Displacement as a function of, time., , In the figure 8.1 (a), displacements of, various particles along a sinusoidal wave, travelling along + ve x-axis are plotted against, their respective distances from the source (at O), at a given instant. This plot is valid for transverse, as well as longitudinal wave. The state of, oscillation of a particle is called its phase. In, order to describe the phase at a place, we need to, know (a) the displacement (b) the direction of, velocity and (c) the oscillation number (during, which oscillation) of the particle there. In Fig., 8.1 (a), particles P and Q (or E and C or B and, D) have same displacements but the directions of, the their velocities are opposite. Particles B and, F have same magnitude of displacements and, same direction of velocity. Such particles are, said to be in phase during their respective, oscillations. Also, these are successive particles, with this property of having same phase., KSA/ XII/ RBG/ 2021/Sound, , Separation between these two particles is, wavelength . These two uccessive particles, differ by '1' in their oscillation number, i.e., if, particle B is at its nth oscillation, particle F will, be at its (n +1)th oscillation as the wave is, travelling along + x direction. Most convenient, way to understand phase is in terms of angle. For, a sinusoidal wave, the variation in the, displacement is a 'sine' function of distance, from the source and of time as discussed below., For such waves it is possible for us to assign, angles corresponding to the displacement (or, time)., At the instant the above graph is drawn,, the disturbance (energy) has just reached the, particle A. The phase angle corresponding, to this particle A can be taken as 00. At this, instant, particle B has completed quarter, oscillation and reached its positive maximum, (sin  = +1). The phase angle  of this particle, B is c/2 = 900 at this instant. Similarly, phase, angles of particles C and E are c (1800) and, 2c(3600) respectively. Particle F has completed, one oscillation and is at its positive maximum, during its second oscillation. Hence its phase,  c 5 c, c, =, angle is 2 +, 2, 2, Que – Obtain the relation between velocity,, wavelength and frequency In one period (T) wave covers a distance, equal to one wavelength (). Hence the velocity, of wave is given by, Velocity =, V =, , , T, , dis tan ce cov ered, Time, 1, But, = n = Frequency, T, ,  V = n, velocity = frequency x wavelength, This is the relation between velocity,, frequency and wavelength, , Simple harmonic progressive wave –, 2

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Waves which continuously travel in a, given direction constant velocity in called, progressive wave., The waves reach different particles of the, medium at different time instants. Hence there is, a phase difference between the vibrations of, different particles of the medium though all, particles vibrate with the same period and, amplitude, Que – State any four Characteristics of S.H., Progressive waves, 1. They transfer energy through the, medium., 2. Particles of the medium are not carried, along with the waves, 3. They are periodic in space and periodic in, time, 4. All the particle in the medium are set into, vibrations about their mean position., 5. All the particles in the medium vibrates, with same amplitude and same period, 6. The intensity at a point is directly, proportional to the square of the, amplitude, 7. Wave can be reflected & refracted., 8.3 Transverse Waves and Longitudinal, Waves:, Progressive waves can be of two types,, transverse and longitudinal waves., Transverse waves :, A wave in which particles of the medium, vibrate in a direction perpendicular to the, direction of propagation of wave is called, transverse wave. e.g. Water waves are transverse, waves, as water molecules vibrate perpendicular, to the surface of water while the wave, propagates along the surface., Characteristics of transverse waves., 1. All particles of the medium in the path of, the wave vibrate in a direction, perpendicular to the direction of, , KSA/ XII/ RBG/ 2021/Sound, , propagation of the wave with same period, and amplitude., 2. During propagation the medium is, divided into alternate the crests and, troughs., 3. Crest and through are alternately, produced., 4. One crest and an adjacent one trough, form one a transverse wave., 5. The distance measured along the wave, between any two consecutive points in, the same phase (crest or trough) is called, the wavelength of the wave., 6. Crests and troughs advance in the, medium and are responsible for transfer, of energy., 7. Transverse waves can travel through, solids and on surfaces of liquids only., 8. They can not travel through liquids and, gases., 9. During propagation there is no change in, the pressure and density at any point of, medium, however shape changes, periodically., 10. All the particles since are constrained in, a single plane, then the wave is called, polarised wave. It can be polarised., 11. Medium conveying a transverse wave, must possess elasticity of shape., Longitudinal waves :, A wave in which particles of the medium, vibrate in a direction parallel to the direction of, propagation of wave is called longitudinal wave., e.g. Sound waves are longitudinal waves., Characteristics of longitudinal waves:, 1. All the particles of medium along the path, of the wave vibrate in a direction parallel, to the direction of propagation of wave, with same period and amplitude., 2. During propagation the medium is, divided into alternate the compressions, and rarefactions., , 3

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3. One compressions and one rarefactions, are alternately produced., 4. One compressions and an adjacent one, rarefactions form one a longitudinal, wave., 5. The distance measured along the wave, between any two consecutive points in, the same phase (compressions or, rarefactions) is called the wavelength of, the wave., 6. compressions and rarefactions advance, in the medium and are responsible for, transfer of energy., 7. It can travel through solids, liquids and, gases., 8. During propagation there is change in the, pressure and density at any point of, medium, however shape changes, periodically., 9. It can not be polarised., When a mechanical wave passes through an, elastic medium, the displacement of any, particle of the medium at a space point x at time, t is given by the expression, y ( x, t ) = f ( x - vt ) ------------ ( 1 ), where v is the speed at which the disturbance, travels through the medium to the right, (increasing x). The factor ( x - vt ) appears, because the disturbance produced at the point, x = 0 at time t reaches the point x = x′ or we say, that the disturbance of the particle at time t at, position x = x′, Thus Eq. ( 1 ) represents a progressive, wave travelling in the positive x-direction with, a constant speed v. The function f depends on, the motion of the source of disturbance. If the, source of disturbance is performing simple, harmonic motion, the wave is represented as a, sine or cosine function of (x - vt) multiplied by, a term which will make (x - vt) dimensionless., Generally we represent such a wave by the, following equation, y ( x, t ) = A sin (Kx -t), KSA/ XII/ RBG/ 2021/Sound, , where A is the amplitude of the wave, k = 2π/λ, is the wave number, λ and ω are the wavelength, and the angular frequency of the wave and, v =ω /k is the speed. The SI units of k, λ and ω, are rad m-1, m and rad s-1 respectively. If T is, the time period of oscillation, then, n = 1/T = ω /(2π) is the frequency of oscillation, measured in Hz (s-1). If the wave is travelling, to the left i.e., along the negative x-direction,, then the equation for the disturbance is, y ( x, t ) = A sin (Kx + t), 8.5 The Speed of Travelling Waves, Speed of a mechanical wave depends, upon the elastic properties and density of the, medium., 8.5.1 The speed of transverse waves, The waves produced on a string are, transverse waves. In this case the restoring force, is provided by the tension T in the string., T, v =, --- (8.6), m, where m is mass per unit length., T is tension, The speed of a transverse wave depends, only on the properties of the string, T and m. It, does not depend on, wavelength or frequency of the wave., 8.5.3 Newton’s formula for velocity of sound:, 1. Sound waves travel through a medium in the, form of compressions and rarefactions., 2. The density of medium is greater at the, compression while being smaller in the, rarefaction. Hence the velocity of sound, depends on elasticity and density of the, medium., 3. This change in pressure & density is, isothermal., Newton formulated the relation as, E, K, =, v=, --- (8.7), , , , , , 4

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where E is the modulus of elasticity of, medium and  is the density of medium., Newton assumed that, during propagation of, sound,, 4. there is no change in the average temperature, of the medium. Hence sound wave, propagation in air is an isothermal process, (temperature remaining constant ) and, isothermal elasticity should be considered., 5. The volume elasticity of air determined, under isothermal change is called isothermal, bulk modulus and is equal to the atmospheric, pressure ‘P’. Hence Newtons formula for, speed of sound in air is given by, 6. v =, , P, , , , --- (8.8), , As atmospheric pressure is given by P=hdg, and at NTP,, h = 0.76 m of Hg, d = 13600 kg/m3-density of mercury,  = 1.293 kg/m3- density of air, and g = 9.8 m/s2, 0.76  13600  9.8, 1.293, v = 279.9 m/s at NTP., 7. This value is 16% less than experimental, value., This is the value of velocity of sound, according to Newton’s formula., , v=, , Necessity for correction to Newtons formula, 1. The experimental value of velocity of sound, at 00C is 332 m/s., 2. The Experimental value is 16% greater than, the value given by the formula. Newton, could not give satisfactory explanation of this, discrepancy., 3. There is necessity of correction of formula. It, was resolved by French physicist Pierre, Simon Laplace (1749-1827)., 4. Scientist Simon Laplace (1749-1827), suggest the correction to this formula., , KSA/ XII/ RBG/ 2021/Sound, , Example 8.2: Suppose you are listening to an, out-door live concert sitting at a distance of 150, m from the speakers. Your friend is listening to, the live broadcast of the concert in another, country and the radio signal has to travel 3000, km to reach him. Who will hear the music first, and what will be the time difference between the, two? Velocity of light =3×108 m/s and thatof, sound is 330m/s., Solution: Time taken by sound to reach you =, 150, s = 0.4546, 330, Time taken by the broadcasted sound (which is, done by EM waves having velocity =3×108m/s), 3  103, 3000km, =, =, = 10-2s, 5, 5, 3  10, 3  10 km / s, ∴ your friend will hear the sound first. The time, difference will be, = 0.4546 - 0.01, = 0.4446 s., 8.5.4 Laplace’s correction, According to Laplace,, 1. The generation of compression and, rarefaction is not a slow process but is a, rapid process., 2. Heat is produced during compression and is, lost during rarefaction., 3. This heat does not get sufficient time for, dissipation., 4. Hence the process is an adiabatic process, and not isothermal & hence, adiabatic, elasticity must be adiabatic and not, isothermal elasticity, as was assumed by, Newton. comp T & as RT , 5. Also air is bad conductor of heat, at, compression, temp., increases, and, rarefaction temp. decreases., 6. The adiabatic modulus of elasticity of air is, given by,, E = P, --- (8.9), where P is the pressure of the medium, (air) and  is ratio of specific heat of air at, constant pressure (Cp) to the specific heat, 5

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of air at constant volume (Cv) called as, the adiabatic ratio, C, i.e.,  = P --- (8.10), CV, , 7., , For air the ratio of Cp / Cv is 1.41, i.e.  = 1.41, Newton's formula for speed of sound in air, as modified by Laplace to give, v=, , 8., , P, , , --- (8.11), , According to this formula velocity of sound, at NTP is, , 1.41 0.76  13600  9.8, 1.293, = 332.3 m/s, This value is in close with the, experimental value. As seen above, the velocity, of sound depends on the properties of the, medium., , v=, , 8.5.5 Factors affecting speed of sound:, As sound waves travel through, atmosphere (open air), some factors related to air, affect the speed of sound., a) Effect of pressure on velocity of sound, According to Laplace’s formula velocity, of sound in air is, v=, , P, , , If M is the mass and V is volume of air then, M, =, , v=, ,  PV, , --- (8.12), M, At constant temperature PV = constant, according to Boyle’s law. Also M and  are, constant, hence v = constant., Therefore at constant temperature, a, change in pressure has no effect on velocity of, sound in air., For ideal gas equation, PV = nRT,, n being the number of moles., KSA/ XII/ RBG/ 2021/Sound, ,  nRT, , v =, , --- (8.13), M, Hence for gaseous medium obeying ideal gas, equation change in pressure has no effect on, velocity of sound unless there is change in, temperature., (b) Effect of temperature on speed of sound, Suppose vo and v are the speeds of sound, at T0 and T in kelvin respectively. Let 0 and , be the densities of gas at these two temperatures., The velocity of sound at temperature T0 and T, can be written by using Eq. (8.13),, v0 =, v=, , , ,  RT0, M, , --- M is molar mass, n = 1, ,  RT, M, , v, =, v0, , RT, RT0, , v, T, =, v0, T0, , --- (8.14), , This equation shows that speed of sound in air is, directly proportional to the square root of, absolute temperature. Thus, speed of sound in air, increases with increase in temperature. Taking, To= 273 K and writing T= (273 + t) K where t, is the temperature in degree celsius. The ratio of, velocity of sound in air at t 0C to that at 00C is, given by,, , , v, 273 + t, =, v0, 273, , , , v, t, = 1+, v0, 273, , , , 1, v, = 1 +  t where  =, 273, v0, , or, v = v0 (1 +  t ), , 1, 2, , As  is very small,we can write,  1 , v = v0 1 +  t ,  2 , , 6

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 1 1 , v = v0  1 + , t,  2 273 , t , , v = v0  1 +, ,  546 , But v0 = 332 m/s at 00C, 332,  v = v0 +, t, 546, v = v0 + (0.61)t, --- (8.15), i.e., for 10 C rise in temperature velocity, increases by 0.61 m/s. Hence for small variations, in temperature (< 500 C), the speed of sound, changes linearly with temperature., , (c) Effect of humidity on speed of sound, Humidity (moisture) in air depends upon, the presence of water vapour in it. Let m and d, be the densities of moist and dry air respectively., If vm and vd are the speeds of sound in moist air, and dry air then using Eq. (8.11)., vm =, , P, m, , and vd =, , P, d, , , , vm, =, vd, , Pd, , m, , --- (8.16), , Moist air is always less dense than dry air,, i.e., m < d, (m = 0.81 kg/m3 (at 00 C) and d= 1.29 kg/m3, (at 00 C)),  vm > vd., Thus, the speed of sound in moist air is, greater than speed of sound in dry air. i.e speed, increases with increase in the moistness of air., , 8.7.1 Echo:, An echo is the repetition of the original, sound because of reflection from some rigid, surface at a distance from the source of sound., , KSA/ XII/ RBG/ 2021/Sound, , If we shout in a hilly region, we are likely, to hear echo., Why can’t we hear an echo at every place?, At 220C, the velocity of sound in air is, 344 m/s. Our brain retains sound for 0.1 second., Thus for us to hear a distinct echo, the sound, should take more than 0.1s after starting from the, source (i.e., from us) to get reflected and come, back to us., distance = speed × time, = 344 × 0.1, = 34.4 m., To be able to hear a distinct echo, the, reflecting surface should be at a minimum, distance of half of the above distance i.e 17.2 m., As velocity depends on the temperature of air,, this distance will change with temperature., 8.8 Qualities of sound:, Audible sound or human response to sound:, Major qualities of sound that are of our, interest are, (i), Pitch,, (ii), Timbre or quality and, (iii) Loudness., (i) Pitch:, i. Pitch refers to the sharpness or shrillness, of the sound., ii. Increase in frequency of sound result is, increase in the pitch and the sound is said to be, sharper., iii. Tone refers to the single frequency of wave., iv. A note may contain single or multiple tone, v . High frequency is generally referred as high, pitch or high tone., vi. Generally speech, of the men is of low pitch, (shrill) and hat of the women is of high pitch, (sharp). Tones of an acoustic guitar are sharper, than that of a base guitar. Sound of table is, sharper than that of a dagga., (ii) Timbre (sound quality), i. Timbre of sound refers to the quality of the, sound which depends upon the mixture of tones, and overtones in the sound., 7

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ii. Same sound played on different musical, instruments feels significantly different and the, musical instrument from which the sound, generated can be easily identified., (iii) Loudness:, i. Loudness depends upon the intensity of, loudness., ii. Intensity of a wave is proportional to square, of the amplitude (I α A2) and is measured in, the (S.I.) unit of W/m2., iii. The human response to intensity is not, linear, i.e., a sound of double intensity is louder, but not doubly loud., iv. Under ideal conditions, for a perfectly, healthy human ear, the least audible intensity is, I0 = 10-12 W/m2. Loudness of a sound of, intensity, v. Loudness of a sound of a intensity I, (measured in unit bel) is given by, Lbel = log10 [ I/IO ], vi. Decibel is the commonly used unit for, loudness., Popular or commonly used unit for, loudness is, decibel., We know, 1 decimetre or 1 dm = 0.1m., Similarly, 1 decibel or 1 db = 0.1 bel., ∴1, bel = 10 db. Thus, loudness in db is 10 times, loudness in bel, Hence, loudness of 20 db sound is felt, double that of 10 db, but its intensity is 10, times that of the 10 db sound. Now, we feel 40, db sound twice as loud as 20 db sound but its, intensity is 100 times as that of 20 db sound, and 10000 times that of 10 db sound. This is the, power of logarithmic or exponential scale., If we move away from a (practically) point, source, the intensity of its sound varies inversely, with square of the distance,, i.e., I α 1 / r2, Whenever you are using earphones or jam, your mobile at your ear, the distance from the, source is too small. Obviously, such a habit for, a long time can affect your normal hearing., , KSA/ XII/ RBG/ 2021/Sound, , Doppler effect –, Que-State and explain Doppler effect in sound, Whenever there is a relative motion, between source of sound and observer. There is, apparent change in frequency of sound heard by, observer is called Doppler effect., This phenomenon can be observed in, both transverse as well as longitudinal waves, The frequency heard by the observer is, called apparent frequency & is given by, V  V0 ,  x n,  V Vs , , na = , Where, , V - velocity of sound, V0 – velocity of observer, VS – velocity of source, n - original frequency of sound, 1. In above equation upper signs are used if, the observer and source of sound are, moving towards each other. In this case, apparent frequency is greater than actual, frequency of source of sound (na > n), 2. In above equation lower signs are used if, the observer and source of sound are, moving away from each other. In this, case apparent frequency is smaller than, actual frequency of source of sound, (na < n), 3. Above equation is applicable only if, observer and source of sound moving, along the same straight line., , Applications of Doppler effect A) To determine speed of aroplanes,, artificial satellites using RADAR (Radio, detection and Ranging), B) To determine speed of stars, C) To determine speed of rotation of sun, D) For speed detection on highways, E) In medical field – In echocardiography, and ultrasonic study of blood vessel, Limitations -, , 8

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1. It is applicable when velocity of observer, and source of sound are much less than, velocity of sound, i.e. V0 and VS < V, 2. Apparent frequency heard by observer is, affected by direction of wind, 3. The motion of observer and source are, along a same straight path, , Once again upper sign is to be used, during relative approach while lower sign is to, be used during relative recede., E) If velocities of source and observer, (listener) are not along the same line their, respective components along the line, joining them should be chosen for, longitudinal Doppler effect and the same, mathematical treatment is applicable., , Common Properties between Doppler, Effect of Sound and Light:, A) Wherever there is relative motion, between listener (or observer) and source, (of sound or light waves), the recorded, frequency is different than the emitted, frequency., B) Recorded frequency is higher (than, emitted frequency), if there is relative, approach., C) Recorded frequency is lower, if there is, relative recede., D) If vL or vs are much smaller then wave, speed (speed of sound or light) we can use, vr as relative velocity. In this case, using, Eq. (8.24), n Vr , n V , where n is Doppler shift or change in the, recorded frequency, i.e., |n - no| and  is, the recorded change in wavelength., n − n0 Vr, , n, V,  V ,  n = n0 1  r ,  V , , Major Differences between Doppler, Effects of Sound and Light:, A) As the speed of light is absolute, onlyrelative, velocity between the observer and the source, matters, i.e., who is in motion is not relevant., B) Classical and relativistic Doppler effects are, different in the case of light, while in case of, sound, it is only classical., C) For obtaining exact Doppler shift for sound, waves, it is absolutely important to know, who is in motion., D) If wind is present, its velocity alters the speed, of sound and hence affects the Doppler shift., In this case, component of the wind velocity, (vw) is chosen along the line joining source, and observer. This is to be algebraically, added with the velocity of sound. Hence 'v' is, to be replaced by (v  vw) in all the above, expressions. Positive sign to be used if v and, vw are along the same direction (remember, that v is always positive and always from, source to listener). Negative sign is to be used, if v and vw are oppositely directed., , 1. Speed of sound wave in air is v = n, 2. The ratio of speed of sound in two media is, v1, , = 1, v2, 2, , 5. Propagation constant of the medium is, 2, K=, , 6. The equation of a simple harmonic, , 3. The particle velocity is VP =  A2 − x 2, 4. The phase angle of a progressive wave is,, 2 x, 2 t, =, =, , T, , KSA/ XII/ RBG/ 2021/Sound, , progressive is, , t, , x, , i) y = A sin 2  − , T  , ii) y = A sin (t - Kx), , 7. Velocity of sound wave is, , v=, , E, , , 9

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8. Velocity of transverse wave is v =, , T, m, , n = n1 – n2, , 9. Beat frequency is,, , v v , , 0, 10. Apparent frequency is na = n , , v, v, s , , 11. The distance between source and reflecting, , surface is,, , d=, , 12. Musical interval =, , vt, 2, , n2, Octave : If n2 = 2n1, n1, , 1. For increasing frequencies nL = nf + (L - 1) x, 2. For decreasing frequencies nL = nF – (L - 1)x, When nL – frequencies of last fork, nf – frequencies of first fork, x – beats per sec. between any two, successive forks., 1. On loading a tuning fork, its frequency, decreases., 2. On filling a tuning fork, its frequency, increases, , 13. When L tuning forks are arranged in order of, , Exercises, 1. Choose the correct alternatives, 1. A sound carried by air from a sitar to a, listener is a wave of following type., (A) Longitudinal stationary, (B)Transverse progressive, (C) Transverse stationary, (D) Longitudinal progressive, 2. When sound waves travel from air to water,, which of these remains constant ?, (A) Velocity, (B) Frequency, (C) Wavelength, (D) All of above, 3. The Laplace’s correction in the expression, for velocity of sound given by Newton is, needed because sound waves, (A) are longitudinal, (B) propagate isothermally, (C) propagate adiabatically, (D) are of long wavelength, 4. Speed of sound is maximum in, (A) air, (B) water, (C) vacuum, (D) solid, 5. The walls of the hall built for music concerns, should, (A) amplify sound (B) reflect sound, (C) transmit sound (D) absorb sound, Solve the following problems., 1. A certain sound wave in air has a speed 340, m/s and wavelength 1.7 m for this wave,, calculate, a) the frequency, b) the period., KSA/ XII/ RBG/ 2021/Sound, , 2., , 3., , 4., , 5., , 6., , 7., , [Ans a) 200 Hz, b) 0.005s], A tuning fork of frequency 170 Hz produces, sound waves of wavelength 2 m. Calculate, speed of sound., [Ans: 340 m/s], An echo-sounder in a fishing boat receives an, echo from a shoal of fish 0.45 s after it was, sent. If the speed of sound in water is 1500, m/s, how deep is the shoal?, [Ans : 337.5 m], A girl stands 170 m away from a high wall, and claps her hands at a steady rate so that, each clap coincides with the echo of the one, before., a) If she makes 60 claps in 1 minute,, what value should be the speed of sound, in air?, b) Now, she moves to another location, and finds that she should now make, 45 claps in 1 minute to coincide with, successive echoes. Calculate her distance, for the new position from the wall., [Ans: a) 340 m/s b) 255 m], Sound wave A has period 0.015 s, sound, wave B has period 0.025. Which sound has, greater frequency?, [Ans : A], At what temperature will the speed of sound, in air be 1.75 times its speed at N.T.P?, [Ans: 836 k = 5630 C], A man standing between 2 parallel eliffs fires, a gun. He hearns two echos one after 3, seconds and other after 5 seconds. The, 10

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separation between the two cliffs is 1360 m,, what is the speed of sound? [Ans:340m/s], 8. If the velocity of sound in air at a given place, on two different days of a given week are in, the ratio of 1:1.1. Assuming the temperatures, on the two days to be same what quantitative, conclusion can your draw about the condition, on the two days?, [Ans: Air is moist on one day and, dry = 1.12 moist = 1.21 moist ], 9. A police car travels towards a stationary, observer at a speed of 15 m/s. The siren on, the car emits a sound of frequency 250 Hz., Calculate the recorded frequency. The speed, of sound is 340 m/s., [Ans : 261.54 Hz], 10. The sound emitted from the siren of an, ambulance has frequency of 1500 Hz. The, speed of sound is 340 m/s. Calculate the, difference in frequencies heard by a, stationary observer it the ambulance initially., travels towards and then away from the, observer at a speed of 30 m/s., [Ans : 1645-2676 Hz], , KSA/ XII/ RBG/ 2021/Sound, , 11

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8.6 Principle of Superposition of Waves:, When two or more waves travelling, through a medium arrive at a point of medium, simultaneously, each wave produces its own, displacement at that point independent of the, others. Hence the resultant displacement at that, point is equal to the vector sum of the, displacements due to all the waves., , KSA/ XII/ RBG/ 2021/Sound, , 12