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PH YSICS HIGHER SECONDARY FIRST YEAR VOLUME - II Revised based on the recommendation of the Textbook Development Committee Untouchability is a sin Untouchability is a crime Untouchability is inhuman TAMILNADU TEXTBOOK CORPORATION COLLEGE ROAD, CHENNAI - 600 006 c Government of Tamilnadu First edition - 2004 Revised edition - 2007 CHAIRPERSON Dr. S. GUNASEKARAN Reader Post Graduate and Research Department of Physics Pachaiyappa’s College, Chennai - 600 030 Reviewers S. RASARASAN P.G .Assistant in Physics P. SARVAJANA RAJAN Govt. Hr. Sec. School Selection Grade Lecturer in Physics Kodambakkam, Chennai - 600 024 Govt.Arts College Nandanam, Chennai - 600 035 GIRIJA RAMANUJAM P.G .Assistant in Physics S. KEMASARI Govt. Girls’ Hr. Sec. School Selection Grade Lecturer in Physics Ashok Nagar, Chennai - 600 083 Queen Mary’s College (Autonomous) Chennai - 600 004 P. LOGANATHAN P.G .Assistant in Physics Dr. K. MANIMEGALAI Govt. Girls’ Hr. Sec. School Reader (Physics) Tiruchengode - 637 211 The Ethiraj College for Women Namakkal District Chennai - 600 008 Dr .R. RAJKUMAR P.G .Assistant in Physics Dharmamurthi Rao Bahadur Calavala Authors Cunnan Chetty’s Hr. Sec. School Chennai - 600 011 S. PONNUSAMY Asst. Professor of Physics Dr .N. VIJAYAN S.R.M. Engineering College Principal S.R.M. Institute of Science and Technology Zion Matric Hr. Sec. School (Deemed University) Selaiyur Kattankulathur - 603 203 Chennai - 600 073 Price Rs. This book has been prepared by the Directorate of School Education on behalf of the Government of Tamilnadu The book has been printed on 60 GSM paper Preface The most important and crucial stage of school education is the higher secondary level. This is the transition level from a generalised curriculum to a discipline-based curriculum. In order to pursue their career in basic sciences and professional courses, students take up Physics as one of the subjects. To provide them sufficient background to meet the challenges of academic and professional streams, the Physics textbook for Std. XI has been reformed, updated and designed to include basic information on all topics. Each chapter starts with an introduction, followed by subject matter. All the topics are presented with clear and concise treatments. The chapters end with solved problems and self evaluation questions. Understanding the concepts is more important than memorising. Hence it is intended to make the students understand the subject thoroughly so that they can put forth their ideas clearly. In order to make the learning of Physics more interesting, application of concepts in real life situations are presented in this book. Due importance has been given to develop in the students, experimental and observation skills. Their learning experience would make them to appreciate the role of Physics towards the improvement of our society. The following are the salient features of the text book. The data has been systematically updated. (cid:78) Figures are neatly presented. (cid:78) Self-evaluation questions (only samples) are included to sharpen (cid:78) the reasoning ability of the student. As Physics cannot be understood without the basic knowledge (cid:78) of Mathematics, few basic ideas and formulae in Mathematics are given. While preparing for the examination, students should not restrict themselves, only to the questions/problems given in the self evaluation. They must be prepared to answer the questions and problems from the text/syllabus. Sincere thanks to Indian Space Research Organisation (ISRO) for providing valuable information regarding the Indian satellite programme. – Dr. S. Gunasekaran Chairperson CONTENTS Page No. 6. Oscillations ............................................. 1 7. Wave Motion ........................................... 39 8. Heat and Thermodynamics .................... 85 9. Ray Optics............................................... 134 10. Magnetism ............................................... 173 Annexure................................................. 206 Logarithmic and other tables ................ 208 6. Oscillations Any motion that repeats itself after regular intervals of time is known as a periodic motion. The examples of periodic motion are the motion of planets around the Sun, motion of hands of a clock, motion of the balance wheel of a watch, motion of Halley’s comet around the Sun observable on the Earth once in 76 years. If a body moves back and forth repeatedly about a mean position, it is said to possess oscillatory motion. Vibrations of guitar strings, motion of a pendulum bob, vibrations of a tuning fork, oscillations of mass suspended from a spring, vibrations of diaphragm in telephones and speaker system and freely suspended springs are few examples of oscillatory motion. In all the above cases of vibrations of bodies, the path of vibration is always directed towards the mean or equilibrium position. The oscillations can be expressed in terms of simple harmonic functions like sine or cosine function. A harmonic oscillation of constant amplitude and single frequency is called simple harmonic motion (SHM). 6.1 Simple harmonic motion A A particle is said to execute simple harmonic motion if its acceleration is directly proportional to the displacement from a P fixed point and is always directed towards that point. y Consider a particle P executing SHM along a straight line between A and B about the mean position O (Fig. 6.1). O The acceleration of the particle is always directed towards a fixed point on the line and its magnitude is proportional to the displacement of the particle from this point. (i.e) a α y B By definition a = −ω2 y Fig. 6.1 where ω is a constant known as angular frequency of the Simple simple harmonic motion. The negative sign indicates that the harmonic acceleration is opposite to the direction of displacement. If m motion of a particle is the mass of the particle, restoring force that tends to bring 1 back the particle to the mean position is given by F = −m ω2 y or F = −k y The constant k = m ω2, is called force constant or spring constant. Its unit is N m−1. The restoring force is directed towards the mean position. Thus, simple harmonic motion is defined as oscillatory motion about a fixed point in which the restoring force is always proportional to the displacement and directed always towards that fixed point. 6.1.1 The projection of uniform circular motion on a diameter is SHM Y Consider a particle moving along the circumference of a circle of radius a and P N centre O, with uniform speed v, in a anticlockwise direction as shown in Fig. 6.2. Let XX’ and YY’ be the two perpendicular X/ X O diameters. Suppose the particle is at P after a time t. If ω is the angular velocity, then the angular displacement θ in time t is given by θ = ωt. Y/ From P draw PN perpendicular to YY’. As Fig. 6.2 Projection of the particle moves from X to Y, foot of the uniform circular motion perpendicular N moves from O to Y. As it moves further from Y to X’, then from X’ to Y’ and back again to X, the point N moves from Y to O, from O to Y′ and back again to O. When the particle completes one revolution along the circumference, the point N completes one vibration about the mean position O. The motion of the point N along the diameter YY’ is simple harmonic. Hence, the projection of a uniform circular motion on a diameter of a circle is simple harmonic motion. Displacement in SHM The distance travelled by the vibrating particle at any instant of time t from its mean position is known as displacement. When the particle is at P, the displacement of the particle along Y axis is y (Fig. 6.3). 2 Y ON Then, in ∆ OPN, sin θ = OP N P ON = y = OP sin θ y a y = OP sin ωt (∵ θ = ωt) X/ X since OP = a, the radius of the circle, O the displacement of the vibrating particle is y = a sin ωt ...(1) The amplitude of the vibrating particle Y/ is defined as its maximum displacement from Fig. 6.3 Displacement in SHM the mean position. Velocity in SHM The rate of change of displacement is the velocity of the vibrating particle. Differentiating eqn. (1) with respect to time t dy d = (a sin ωt) v s dt dt o v c ∴ v = a ω cos ωt ...(2) v sin P The velocity v of the particle moving along the circle can also be obtained by a resolving it into two components as shown in Fig. 6.4. (i) v cos θ in a direction parallel to OY (ii) v sin θ in a direction perpendicular to OY The component v sin θ has no effect Fig. 6.4 Velocity in SHM along YOY′ since it is perpendicular to OY. ∴ Velocity = v cos θ = v cos ωt We know that, linear velocity = radius × angular velocity ∴ v = aω ∴ Velocity = aω cos ωt ∴ Velocity = aω 1-sin2ωt 3 Velocity = aω 1-⎛⎜y⎞⎟2 ⎡⎢∵ sin θ = y⎤⎥ ⎝a⎠ ⎣ a⎦ Velocity = ω a2-y2 ...(3) Special cases (i) When the particle is at mean position, (i.e) y = 0. Velocity is aω and is maximum. v = + aω is called velocity amplitude. (ii) When the particle is in the extreme position, (i.e) y = + a, the velocity is zero. Acceleration in SHM The rate of change of velocity is the acceleration of the vibrating particle. d2y d ⎛dy⎞ d = ⎜ ⎟ = (aω cos ωt) = −ω2 a sin ωt. dt2 dt ⎝dt ⎠ dt d2y ∴ acceleration = = –ω2 y ...(4) dt2 The acceleration of the particle can also be obtained by component method. The centripetal v2 cos acceleration of the particle P a v2 acting along PO is . This a v2 v2 sin acceleration is resolved into a a two components as shown in Fig. 6.5. v2 (i) cos θ along PN a perpendicular to OY v2 (ii) sin θ in a direction a Fig. 6.5 Acceleration in SHM parallal to YO 4 The component v2 cos θ has no effect along YOY′ since it is a perpendicular to OY. v2 Hence acceleration = – sin θ a = – a ω2 sin ωt (∵ v = a ω) = − ω2y (∵ y = a sin ωt) ∴ acceleation = − ω2 y The negative sign indicates that the acceleration is always opposite to the direction of displacement and is directed towards the centre. Special Cases (i) When the particle is at the mean position (i.e) y = 0, the acceleration is zero. (ii) When the particle is at the extreme position (i.e) y = +a, acceleration is ∓ a ω2 which is called as acceleration amplitude. The differential equation of simple harmonic motion from eqn. (4) d2y is + ω2 y = 0 ...(5) dt2 Using the above equations, the values of displacement, velocity and acceleration for the SHM are given in the Table 6.1. It will be clear from the above, that at the mean position y = 0, velocity of the particle is maximum but acceleration is zero. At extreme Table 6.1 - Displacement, Velocity and Acceleration Time ωt Displacement Velocity Acceleration a sin ωt aω cos ωt −ω2a sin ωt t = 0 0 0 aω 0 π T t = +a 0 −aω2 4 2 T t = π 0 −aω 0 2 t = 3T 3π −a 0 +aω2 4 2 t = T 2π 0 +aω 0 5 position y = +a, the velocity is zero but the acceleration is maximum 3T ∓a ω2 acting in the opposite direction. 4 y T T Graphical representation of SHM 4 2 Graphical representation of displacement, velocity and acceleration of a particle vibrating simple T harmonically with respect to time t is 2 shown in Fig. 6.6. T 3T 4 4 (i) Displacement graph is a sine curve. Maximum displacement of the particle is y = +a. (ii) The velocity of the vibrating T particle is maximum at the mean 4 position i.e v = + a ω and it is zero at T 3T the extreme position. 2 4 (iii) The acceleration of the vibrating particle is zero at the mean Fig. 6.6 Graphical representation position and maximum at the extreme position (i.e) ∓a ω2. π The velocity is ahead of displacement by a phase angle of . The π 2 acceleration is ahead of the velocity by a phase angle or by a phase 2 π ahead of displacement. (i.e) when the displacement has its greatest positive value, acceleration has its negative maximum value or vice versa. 6.2 Important terms in simple harmonic motion (i) Time period The time taken by a particle to complete one oscillation is called the time period T. In the Fig. 6.2, as the particle P completes one revolution with angular velocity ω, the foot of the perpendicular N drawn to the vertical diameter completes one vibration. Hence T is the time period. 6