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Wave Motion, and Its Applications, , Ee, , INTRODUCTION, —— IN, , Wave motion is Special kind of motion in which there is not any transportation of material, bodies, but only transfer of energy takes place in such motion. Wave motion plays an important, , Tole in our daily life as we use it for communication purposes. Light and sound waves are, Tegarded as messengers of nature., , , , In this chapter, a brief descri, related parameters will be given., , for propagation of wave will be d, , ption of wave motion regarding types of waves and their, Also vibrational motion of particles of medium, responsible, lescribed in sections regarding simple harmonic motion., After reading this chapter, a student will be able to 4, , (i) Define wave motion and describe its types i.e., longitudinal and transverse waves., , (ii) Explain the terms periodic motion, oscillatory motion and simple harmonic motion., , (iii) Derive and explain expressions for displacement,, , velocity, acceleration, time Period, and frequency of a particle executing S.H.M., (ivy) Explain types of vibrations viz. free, forced and resonant vibrations with examples., (v) Explain the principle of Superposition of waves and phenomena related to it,, , (vi) Describe the various applications of ultrasonics in the field of m, , edical sciences and, engineering., , (vii) Learn about the acoustical requirements of good hall or auditorium,, , > 1.1. WAVE MOTION, , : Wave motion is a form of disturbance which travels Sorward in a material medium due to, __ the repeated periodic motion of the particles of the medium about’ their mean Positions and the, Motion being handed over from particle to particle in th, , eae, , e direction of Propagation of wave,, * The propagation of disturbance may be taken as transfer of energy without any transfer of, S or material medium. Waves are mainly of two ty, , pes, namely ;, 1. Mechanical or Elastic waves, 2. Non-mechanical or Electromagnetic waves, ‘, , , , , , , , , 1, , Scanned with CamScanner
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be elastic ; this ow its original shape or configur, , ) Tt must, , er ee, , ‘The particles Jes of the medium m, P ; medium possess inertia /.e., the partic ; umm, , have capacity Pan energy and then transfer it to its succeeding particle., , Examples : Sound waves, water waves, waves in strings or ropes., , Further, the mechanical waves are also divided into two types, namely ;, , (i) Longitudinal waves, (ii) Transverse waves., , 2. Non-mechanical waves : The waves which, propagation are known as non-mechanical waves or, travel in vacuum also., , Examples of this type of waves include all the light waves such as radio waves, microwaves,, , X-rays etc., |, , , , , , , , , , do not require material medium for their, electromagnetic waves. These waves can, , @ 1.1.1. Types of Wave Motion, As described earlier the mechanical waves are of two types /.e.,, , 1. Transverse waves, 2. Longitudinal waves., , 1. TRANSVERSE WAVES : The waves, in which the particles of the medium vibrate, about their mean position in a direction at, right angles to the direction of propagation, of the wave., , Examples : The most familiar examples, of transverse waves are :, , (i) Ripples produced on the surface of, , water when a stone is dropped (see, Fig. 1.1). In this case, the individual, , particles of the medium (water) vibrate up and down i.e., in a oe, direction at right angles to the direction in which the ripples Pm, oe, , travel., (ii) Waves produced in a rope fixed at one end, when given number wx A, , of jerks at the other end (see Fig. 1.2). The continuous jerky, , P, P, motion given to the free end propagates, gradually to Sim,, next part of the rope. Every part (particles of the pe raeek a a, , and down, while the wave train, ae travels forward along the p gam [, , Fig. 1.2., , , , Gig. 4.1., , Scanned with CamScanner
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asmumption that the disurbance tke tine of te oder of 1/4 Wt, le to its succeeding particle. Here, “T” is time period and is equal to time 4, > of the medium to complete its one vibration,, , ew Att = 0, the disturbance reaches fn partici dt aris cag te SP, . The remaining’ particles: are at rest., , (ii) Att = T/4, first particle reaches at upper extreme (U) and due to elastic nature of, hs medium it will be pulled back towards its mean position (O) by second particle, which, in turn also gets disturbed and starts its vibrations by moving in upward direction. —, , (iii) At t = T/2, first and second particles are at mean position and extreme (U) position, __-Tespectively. Particle 2 disturbed the third particle in a similar way as was done by, first particle at ¢ = T/4., , _—s iv):« At ¢ = 37/4, first particle while moving towards mean position, due to inertia overshots, 1 * its mean position and reaches at lower extreme position. Second and third particles are at, mean and upper extreme position respectively. Now, the disturbance reaches at particle 4., , (v) Att = T, the particle 5 gets the disturbance, the positions and directions of motion of, other Sa are as shown in Fig. 1.3., , a, , me be, , , , , , Scanned with CamScanner
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n conclude that elastic, - discuss te for propa features of tanaverse waves are given belOW :, 1. The particles of the medium vibrate in a direction at right aan a — a, propagation of the wave, The amplitude and the time period . a ., 2. Every particle begins to vibrate a little later than its preceding particle i.e., there is |, phase difference between two consecutive particles., 3. The waves travel in the form of crests and troughs, One crest and one trough constitutes, a wave (see Fig. 1.4)., 4. Transverse waves are possible in media which possess elasticity of shape or have a free, surface. Thus, transverse waves are possible in solids and liquids only., , , , 5. There is transfer of energy by these waves., , ® Terms Used for Description of Transverse Waves, , 1. Crest : A portion in the medium at the maximum distance above the mean position is, called a crest (see Fig. 1.4)., , 2. Trough : A portion in the medium at the maximum, distance below the mean position is called a trough (see, , Transverse wave, ni ee, Crest Crest, , , , , , Fig. 1.4)., 3. Wavelength (A) : The distance between two a 7, nearest crests or troughs is called wavelength. It is — | Amplitude 1, denoted by A. ' Wavelength "ough Troms, 4. Wave velocity (v) : The velocity with which e, wave (disturbance) travels (propagates) through medium i at y, , is called wave velocity. It is denoted by v., , 5. Amplitude : Height of crest or depth of trou:, / : i gh from the mean position is called litude., It is the maximum displacement of the particle from the mean position. It is denated 1 «, ys 6. Frequency : The number of vibrations completed in one second it ti is called, requency. It is denoted by n, in, 7. Relation Between Frequency, Wavelength and Wave Velocity A, v.= nhi.e., Waye velocity = Fre, , i quency x Wavelength. “7., 2. LONGITUDINAL WAVE MOTION : The type :, —_—_—_, , in which the particl ae, aon in he pre of th mtn ite a ana A ARAN, , ‘ the directi, propagation (motion) of the wave. trection of, , ee AMIN, , (i) Sound waves travelling in air,, , , , , , , , , , ii) Waves produced in & spring when j, Oe gown (a Fis. ened ee AAAI, , |, ?, &, , el, , , , Scanned with CamScanner
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and Its Applications Ls, , ii) Waves in the stem of a vibrating tuning fork., , iv) Wave motion set up in the engine of a train due to which motion is transferred fron, , engine to the last wagon of the train., , In order to understand the generation and propagation of longitudinal waves, we consider <, segment of material medium represented by five particles as shown in Fig. 1.6, wherein the, state 1-¢., Position and direction of motion of all the particles is shown at various instants of, Eines. Here, it has been assumed that the disturbance takes ‘T/4’ seconds to reach from one, particle to its succeeding particle, where ‘T’ is time period of vibration of any particle of the, medium., , °, , aur, ', ', 1, 1, 1, 1, 1, ', , , , a ee, , L, 1, |, |, |, |, |, |, 1, 1, , |, 1, |, 1, 1, |, , Wee eon Sls eee, as tata et a, , ', ‘, ', ', ', ', ', ', ', ', ', ', ', ', ', ', ', ', ,, t, ', ‘, ', ', I, 1, ', ', 1, ', ', ’, ', ‘, ', ', , I, ', 1, 1, t, 1, 1, 1, 1, 1, ', ', ', 1, 1, i, , , , Fig. 1.6., , (i) Att = 0, all particles are at mean position, marked as ‘O’ and disturbance just reaches, to first particle and it starts vibrating towards right of mean position. The remaining, particles are yet undisturbed (see Fig. 1.6)., , (ii) At t = T/4, particle 1 reaches at right extreme ‘R’ (see Fig. 1.6) and on account of, , elastic forces of repulsion between particles 1 and 2, the particle 2 of medium also, gets disturbed and both the particles, move in opposite directions. Particles 3, 4 and 5, are at rest., , (iii) Att = T/2, the first particle reaches at mean position ‘O’ and second particle reaches, at right extreme and in turn disturbs third particle in a similar way 98 walt Sila, first particle to disturb particle 2. Particles 4 and 5 are at rest,, , (iv) At t = 31/4, the fourth particle is disturbed now, the positions and direction of, motion of first, second and third particles are as shown. Particle 5 is still at rest., , (v) Att = T, the first particle has completed one vibration and particle 5 is now disturbed., The positions and directions of motion of remaining particles are also as shown., , From above description of longitudinal wave motion, one can easily judge the role of, ‘inertia’ of particles i,e., their ability to handle energy and transfer it to ci Ig ea, elastic nature of material medium, the two main requirements for propagation ee Ge in *, , , , Scanned with CamScanner
