# Physics (Theory) Class 11 ISC (Commerce) CISCE Topics and Syllabus

CISCE Syllabus For Class 11 Physics (Theory): Knowing the Syllabus is very important for the students of Class 11. Shaalaa has also provided a list of topics that every student needs to understand.

The CISCE Class 11 Physics (Theory) syllabus for the academic year 2022-2023 is based on the Board's guidelines. Students should read the Class 11 Physics (Theory) Syllabus to learn about the subject's subjects and subtopics.

Students will discover the unit names, chapters under each unit, and subtopics under each chapter in the CISCE Class 11 Physics (Theory) Syllabus pdf 2022-2023. They will also receive a complete practical syllabus for Class 11 Physics (Theory) in addition to this.

## CISCE Class 11 Physics (Theory) Revised Syllabus

CISCE Class 11 Physics (Theory) and their Unit wise marks distribution

## Syllabus

100 Physical World and Measurement

Physical World:

Scope of Physics and its application in everyday life. Nature of physical laws

• Physics and its branches (only basic knowledge required); fundamental laws and fundamental forces in nature (gravitational force, electro-magnetic force, strong and weak nuclear forces; unification of forces). Application of Physics in technology and society (major scientists, their discoveries, inventions and laws/principles to be discussed briefly).

Units and Measurements

Measurement: need for measurement; units of measurement; systems of units: fundamental and derived units in SI; measurement of length, mass and time; accuracy and precision of measuring instruments; errors in measurement; significant figures

Dimensional formulae of physical quantities and constants, dimensional analysis and its applications.

• Importance of measurement in scientific studies; physics is a science of measurement. Unit as a reference standard of measurement; essential properties.
• Systems of units; CGS, FPS, MKS, MKSA, and SI; the seven base units of SI selected by the General Conference of Weights and Measures in 1971 and their definitions, list of fundamental, supplementary and derived physical quantities; their units and symbols (strictly as per rule); subunits and multiple units using prefixes for powers of 10 (from atto for 10-18 to tera for 1012); other common units such as fermi, angstrom (now outdated), light year, astronomical unit and parsec.
• A new unit of mass used in atomic physics is unified atomic mass unit with symbol u (not amu); rules for writing the names of units and their symbols in SI (upper case/lower case.) Derived units (with correct symbols); special names wherever applicable; expression in terms of base units (e.g.: N= kg m/s2)
• Accuracy of measurement, errors in measurement: precision of measuring instruments, instrumental errors, systematic errors, random errors and gross errors. Least count of an instrument and its implication on errors in measurements; absolute error, relative error and percentage error; combination of errors in (a) sum and difference, (b) product and quotient and (c) power of a measured quantity.
• Significant figures; their significance; rules for counting the number of significant figures; rules for (a) addition and subtraction, (b) multiplication/ division; ‘rounding off’ the uncertain digits; order of magnitude as statement of magnitudes in powers of 10; examples from magnitudes of common physical quantities - size, mass, time, etc
• Dimensions of physical quantities; dimensional formula; express derived units in terms of base units (N = kg.m s-2); use symbol […] for dimensions of or base unit of; e.g.: dimensional formula of force in terms of fundamental quantities written as [F] = [MLT–2].Principle of homogeneity of dimensions. Expressions in terms of SI base units and dimensional formula may be obtained for all physical quantities as and when new physical quantities are introduced.
• Use of dimensional analysis to
1. check the dimensional correctness of a formula/ equation;
2. to obtain the dimensional formula of any derived physical quantity including constants;
3. to convert units from one system to another; limitations of dimensional analysis
200 Kinematics

Motion in a Straight Line

Frame of references, Motion in a straight line (one dimension): Position-time graph, speed and velocity.

Elementary concepts of differentiation and integration for describing motion, uniform and non- uniform motion, average speed, velocity, average velocity, instantaneous velocity and uniformly accelerated motion, velocity - time and position - time graphs. Relations for uniformly accelerated motion (graphicaltreatment).

• Frame of reference, concept of point mass, rest and motion; distance and displacement, speed and velocity, average speed and average velocity, uniform velocity, instantaneous speed and instantaneous velocity, acceleration, instantaneous acceleration, s-t, v-t and a-t graphs for uniform acceleration and conclusions drawn from these graphs; kinematic equations of motion for objects in uniformly accelerated rectilinear motion derived using graphical, calculus or analytical method, motion of an object under gravity, (one dimensional motion).
• Differentiation as rate of change; examples from physics – speed, acceleration, velocity gradient, etc. Formulae for differentiation of simple functions: xn , sinx, cosx, ex and ln x. Simple ideas about integration – mainly. ∫xn.dx. Both definite and indefinite integrals to be mentioned (elementary calculus not to be evaluated).

Motion in a Plane

Scalar and Vector quantities with examples. Position and displacement vectors, general vectors and their notations; equality of vectors, addition and subtraction of vectors, relative velocity, Unit vector; resolution of a vector in a plane, rectangular components, Scalar and Vector product of two vectors. Projectile motion and uniform circular motion

General Vectors and notation, position and displacement vector. Vectors explained using displacement as a prototype - along a straight line (one dimensional), on a plane surface (two dimensional) and in an open space not confined to a line or a plane (three dimensional); symbol and representation; a scalar quantity, its representation and unit, equality of vectors. Unit vectors denoted by hati,hatj,hatk orthogonal unit vectors along x, y and z axes respectively.

Examples of one dimensional vector

vec (V_1)=ahati  where a, b, c are scalar quantities or numbers;

vec (V_2)=ahati+bhatj is a two dimensional or planar vector

vec (V_3) = a hati+bhatj+chatk is a three dimensional or space vector. Concept of null vector and co-planar vectors

Addition: use displacement as an example; obtain triangle law of addition; graphical and analytical treatment; Discuss commutative and associative properties of vector addition (Proof not required). Parallelogram Law; sum and difference; derive expressions for magnitude and direction from parallelogram law; special cases; subtraction as special case of addition with direction reversed; use of Triangle Law for subtraction also; if vec a+vec b=vecc;vecc-  In a parallelogram, if one diagonal is the sum, the other diagonal is the difference; addition and subtraction with vectors expressed in terms of unit vectors hati,hatj,hatk multiplication of a vector by a real number.

Use triangle law of addition to express a vector in terms of its components. if

veca+vecb=vecc is an addition fact, vec c=veca+vecb is a resolution; vec a are components of vecc . Rectangular components, relation between components, resultant and angle between them. Dot (or scalar) product of vectors  veca.vecb=abcostheta . example W = vecF.vecS=FScostheta

Special case of Θ = 0o , 90º and 180º . Vector (or cross) product

vecaxxvecb=[ab sintheta]hatn; example: torque  vect=vecrxxvecF; Special cases using unit vectors hati,hatj,hatk

Concept of relative velocity, start from simple examples on relative velocity of one dimensional motion and then two dimensional motion; consider displacement first; relative displacement (use Triangle Law or parallelogram Law).

Various terms related to projectile motion; obtain equations of trajectory, time of flight, maximum height, horizontal range, instantaneous velocity, [projectile motion on an inclined plane not included]. Examples of projectile motion.

Examples of uniform circular motion: details to be covered in unit 3 (d)

300 Laws of Motion

General concept of force, inertia, Newton's first law of motion; momentum and Newton's second law of motion; impulse; Newton's third law of motion.

Law of conservation of linear momentum and itsapplications.

Equilibrium of concurrent forces. Friction: Static and kinetic friction, laws of friction, rolling friction, lubrication.

Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on a level circular road, vehicle on a banked road).

• (a)Newton's first law: Statement and explanation; concept of inertia, mass, force; law of inertia; mathematically, if ∑F=0, a=0.
• Newton's second law: vecp=mvecv;vecFalpha(dvecp)/dt;vecF=k(dvecp)/dt
• Define unit of force so that k=1; vecF=(dvecp)/dt; a vector equation. For classical physics with v not large and mass m remaining constant, obtain vecF=mveca For v → c, m is not constant. Then m=m_o/sqrt((1-v^2)/c^2) . Note that F= ma is the special case for classical mechanics. It is a vector equation. veca||vecF . Also, this can be resolved into three scalar equations Fx=max etc. Application to numerical problems; introduce tension force, normal reaction force. If a = 0 (body in equilibrium), F= 0. Statement, derivation and explanation of principle of conservation of linear momentum. Impulse of a force: FΔt =Δp.
• Newton's third law. Obtain it using Law of Conservation of linear momentum. Proof of Newton’s second law as real law. Systematic solution of problems in mechanics; isolate a part of a system, identify all forces acting on it; draw a free body diagram representing the part as a point and representing all forces by line segments, solve for resultant force which is equal to mveca . Simple problems on “Connected bodies” (not involving two pulleys).
• (b) Force diagrams; resultant or net force from Triangle law of Forces, parallelogram law or resolution of forces.
• Apply net force SigmavecF=mveca . Again for equilibrium a=0 and ΣF=0. Conditions of equilibrium of a rigid body under three coplanar forces. Discuss ladder problem.
• (c) Friction; classical view and modern view of friction, static friction a self-adjusting force; limiting value; kinetic friction or sliding friction; rolling friction, examples.
• Laws of friction: Two laws of static friction; (similar) two laws of kinetic friction; coefficient of friction μs = fs(max)/N and μ= fk/N graphs.
• Friction as a non-conservative force; motion under friction, net force in Newton’s 2nd law is calculated including fk. Motion along a rough inclined plane – both up and down. Pulling and pushing of a roller. Angle of friction and angle of repose. Lubrication, use of bearings, streamlining, etc.
• (d) Angular displacement (Θ), angular velocity (ω), angular acceleration (α) and their relations. Concept of centripetal acceleration; obtain an expression for this acceleration using Deltavecv . Magnitude and direction of a same as that of Deltavecv ; Centripetal acceleration; the cause of this acceleration is a force - also called centripetal force; the name only indicates its direction, it is not a new type of force, motion in a vertical circle; banking of road and railway track (conical pendulum is excluded).

400 Work, Power and Energy

Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power.

Potential energy, potential energy of a spring, conservative forces: conservation of mechanical energy (kinetic and potential energies); Conservative and non-conservative forces. Concept of collision: elastic and inelastic collisions in one and two dimensions.

• Work done W= vecF.vecS=FScostheta.If F is variable dW = vecF.dvecSand
• W = intdw=intvecF.dvecS
• therefore, W=∫FdS is the area under the F- S graph or if F can be expressed in terms of S, ∫FdS can be evaluated. Example, work done in stretching a spring W = ∫Fdx = ∫kxdx = 1/2kx2. This is also the potential energy stored in the stretched spring U=½ kx2.
• Kinetic energy and its expression, Work-Energy theorem E=W. Law of Conservation of Energy; oscillating spring. U+K = E = Kmax = Umax (for U = 0 and K = 0 respectively); graph different forms of energy and their transformations. E = mc2 (no derivation).
• Power P=W/t; P = vecF.vecv.
• Collision in one dimension; derivation of velocity equation for general case of m1 ≠ m2 and u1 ≠ u2=0; Special cases for m1=m2=m; m1>>m2 or m1<<m2. Oblique collisions i.e. collision in two dimensions.
500 Motion of System of Particles and Rigid Body

Idea of centre of mass: centre of mass of a two- particle system, momentum conservation and centre of mass motion. Centre of mass of a rigid body; centre of mass of a uniform rod.

Moment of a force, torque, angular momentum, laws of conservation of angular momentum and its applications

Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparative study of linear and rotational motions.

Moment of inertia, radius of gyration, moments of inertia for simple geometrical objects (no derivation). Statement of parallel and perpendicular axes theorems and their applications.

Definition of centre of mass (cm), centre of mass (cm) for a two particle system m1x1+m2x2=Mxcm; differentiating, get the equation for vcm and acm; general equation for N particles- many particles system; [need not go into more details];centre of gravity, principle of moment, discuss ladder problem, concept of a rigid body;kinetic energy of a rigid body rotating about a fixed axis in terms of that of the particles of the body; hence, define moment of inertia and radius of gyration; physical significance of moment of inertia; unit and dimension; depends on mass and axis of rotation; it is rotational inertia; equations of rotational motions.

Applications: only expression for the moment of inertia, I (about the symmetry axis) of: (i) a ring; (ii) a solid and a hollow cylinder, (iii) a thin rod (iv) a solid and a hollow sphere, (v) a disc - only formulae (no derivations required)

• Statements of the parallel and perpendicular axes theorems with illustrations [derivation not required]. Simple examples with change of axis.
• Definition of torque (vector); vect=vecrxvecFand angular momentum barL = vecrxvecp
• for a particle (no derivations); differentiate to obtain dbarLsimilar to Newton’s second law of motion (linear);hence τ=I α and L = Iω; (only scalar equation); Law of conservation of angular momentum; simple applications. Comparison of linear and rotational motions.
600 Gravitation

Kepler's laws of planetary motion, universal law of gravitation. Acceleration due to gravity (g) and its variation with altitude, latitude and depth.

Gravitational potential and gravitational potential energy, escape velocity, orbital velocity of a satellite, Geo-stationary satellites.

• Newton's law of universal gravitation; Statement; unit and dimensional formula of universal gravitational constant, G [Cavendish experiment not required]; gravitational acceleration on surface of the earth (g), weight of a body W= mg from F=ma
• Relation between g and G. Derive the expression for variation of g above and below the surface of the earth; graph; mention variation of g with latitude and rotation, (without derivation).
• Gravitational field, intensity of gravitational field and potential at a point in earth’s gravitational field. Vp = Wαp/m. Derive expression (by integration) for the gravitational potential difference ΔV = VB-VA = G.M(1/rA-1/rB); here Vp = V(r) = -GM/r; negative sign for attractive force field; define gravitational potential energy of a mass m in the earth's field;  expression for gravitational potential energy U(r) = Wαp = m.V(r) = -G M m/r; show that ΔU = mgh, for h << R. Relation between intensity and acceleration due to gravity.
• Derive expression for the escape velocity of earth using energy consideration; ve depends on mass of the earth; for moon ve is less as mass of moon is less; consequence - no atmosphere on the moon.
• Satellites (both natural (moon) and artificial) in uniform circular motion around the earth; Derive the expression for orbital velocity and time period; note the centripetal acceleration is caused (or centripetal force is provided) by the force of gravity exerted by the earth on the satellite; the acceleration of the satellite is the acceleration due to gravity [g’= g(R/R+h)2; F’G = mg’]. Weightlessness; geostationary satellites; conditions for satellite to be geostationary; parking orbit, calculation of its radius and height; basic concept of polar satellites and their uses.
• Kepler's laws of planetary motion: explain the three laws using diagrams. Proof of third law (for circular orbits only).
700 Properties of Bulk Matter

Mechanical Properties of Solids:

• Elastic behaviour of solids, Stress-strain relationship, Hooke's law, Young's modulus, bulk modulus, shear modulus of rigidity, Poisson's ratio; elastic energy.
• Elasticity in solids, Hooke’s law, Young modulus and its determination, bulk modulus and shear modulus of rigidity, work done in stretching a wire and strain energy, Poisson’s ratio.

Mechanical Properties of Fluids

Pressure due to a fluid column; Pascal's law and its applications (hydraulic lift and hydraulic brakes), effect of gravity on fluid pressure.

Viscosity, Stokes' law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli's theorem and its applications.

Surface energy and surface tension, angle of contact, excess of pressure across a curved surface, application of surface tension ideas to drops, bubbles and capillary rise.

• Pressure in a fluid, Pascal’s Law and its applications, buoyancy (Archimedes Principle)
• General characteristics of fluid flow; equation of continuity v1a1= v2a2; conditions; applications like use of nozzle at the end of a hose; Bernoulli’s principle (theorem); assumptions - incompressible liquid, streamline (steady) flow, non-viscous and irrotational liquid - ideal liquid; derivation of equation; applications of Bernoulli’s theorem atomizer, dynamic uplift, Venturimeter, Magnus effect etc.
• Streamline and turbulent flow - examples; streamlines do not intersect (like electric and magnetic lines of force); tubes of flow; number of streamlines per unit area  velocity of flow (from equation of continuity v1a1= v2a2); critical velocity; Reynold's number (significance only) Poiseuille’s formula with numericals.
• Viscous drag; Newton's formula for viscosity, co-efficient of viscosity and its units.
• Flow of fluids (liquids and gases), laminar flow, internal friction between layers of fluid, between fluid and the solid with which the fluid is in relative motion; examples; viscous drag is a force of friction; mobile and viscous liquids
• Velocity gradient dv/dx (space rate of change of velocity); viscous drag F = ηA dv/dx; coefficient of viscosity η = F/A (dv/dx) depends on the nature of the liquid and its temperature; units: Ns/m2 and dyn.s/cm2= poise.1 poise=0.1 Ns/m2 .
• Stoke's law, motion of a sphere falling through a fluid, hollow rigid sphere rising to the surface of a liquid, parachute, obtain the expression of terminal velocity; forces acting; viscous drag, a force proportional to velocity; Stoke’s law; v-t graph.
• Surface tension (molecular theory), drops and bubbles, angle of contact, work done in stretching a surface and surface energy, capillary rise, measurement of surface tension by capillary (uniform bore) rise method. Excess pressure across a curved surface, application of surface tension for drops and bubbles.
800 Heat and Thermodynamics

Thermal Properties of Matter: Heat, temperature, thermal expansion; thermal expansion of solids, liquids and gases, anomalous expansion of water; specific heat capacity, calorimetry; change of state, specific latent heat capacity.

Heat transfer-conduction, convection and radiation, thermal conductivity, qualitative ideas of Blackbody radiation, Wein's displacement Law, Stefan's law, and Greenhouseeffect.

• Temperature and Heat, measurement of temperature (scales and inter conversion). Ideal gas equation and absolute temperature, thermal expansion in solids, liquids and gases. Specific heat capacity, calorimetry, change of state, latent heat capacity, steady state and temperature gradient. Thermal conductivity; co-efficient of thermal conductivity, Use of good and poor conductors, Searle’s experiment,(Lee’s Disc method is not required). Convection with examples.
• Black body is now called ideal or cavity radiator and black body radiation is cavity radiation; Stefan’s law is now known as Stefan Boltzmann law as Boltzmann derived it theoretically. There is multiplicity of technical terms related to thermal radiation - radiant intensity I (T) for total radiant power (energy radiated/second) per unit area of the surface, in W/m2 , I (T) =σ T4; dimension and SI unit of σ. For practical radiators I =∈. σ T4 where ∈ (dimension less) is called emissivity of the surface material; ∈=1 for ideal radiators. The Spectral radiancy R(λ). I (T)= int_0^alpha (λ) dλ.
• Graph of R(λ) vs λ for different temperatures. Area under the graph is I (T). The λ corresponding to maximum value of R is called λmax; decreases with increase in temperature.
• Wien’s displacement law; Stefan’s law and Newton’s law of cooling. [Deductions from Stefan’s law not necessary]. Greenhouse effect – self- explanatory.

Thermodynamics.

Thermal equilibrium and definition of temperature (zeroth law of thermodynamics), heat, work and internal energy. First law of thermodynamics, isothermal and adiabatic processes.

Second law of thermodynamics: reversible and irreversible processes, Heat engine and refrigerator.

• Thermal equilibrium and zeroth law of thermodynamics: Self explanatory.
• First law of thermodynamics
• Concept of heat (Q) as the energy that is transferred (due to temperature difference only) and not stored; the energy that is stored in a body or system as potential and kinetic energy is called internal energy (U). Internal energy is a state property (only elementary ideas) whereas, heat is not; first law is a statement of conservation of energy, when, in general, heat (Q) is transferred to a body (system), internal energy (U) of the system changes and some work W is done by the system; then Q=ΔU+W; also W=∫pdV for working substance - an ideal gas; explain the meaning of symbols (with examples) and sign convention carefully (as used in physics: Q>0 when added to a system, ΔU>0 when U increases or temperature rises, and W>0 when work is done by the system). Special cases for Q=0 (adiabatic), ΔU=0 (isothermal) and W=0 (isochoric).
• Isothermal and adiabatic changes in a perfect gas described in terms of PV graphs; PV = constant (Isothermal) and PVγ = constant (adiabatic); joule and calorie relation (derivation of PVγ = constant not required).
• Note that 1 cal = 4.186 J exactly and J (so-called mechanical equivalent of heat) should not be used in equations. In equations, it is understood that each term as well as the LHS and RHS are in the same units; it could be all joules or all calories.
• Derive an expression for work done in isothermal and adiabatic processes; principal and molar heat capacities; Cp and Cv; relation between Cp and Cv (Cp - Cv = R). Work done as area bounded by PV graph.
• Second law of thermodynamics, Carnot's cycle. Some practical applications.
• Only one statement each in terms of Kelvin’s impossible steam engine and Clausius’ impossible refrigerator. Brief explanation of the law. Reversible and irreversible processes, Heat engine; Carnot’s cycle - describe realisation from source and sink of infinite thermal capacity, thermal insulation, etc. Explain using pV graph (isothermal process and adiabatic process) expression and numericals (without derivation) for efficiency η=1- T2/T1., Refrigerator and heat pumps
900 Behaviour of Perfect Gases and Kinetic Theory of Gases

Kinetic Theory: Equation of state of a perfect gas, work done in compressing a gas. Kinetic theory of gases - assumptions, concept of pressure. Kinetic interpretation of temperature; rms speed of gas molecules; degrees of freedom, law of equi-partition of energy (statement only) and application to specific heat capacities of gases; concept of mean free path, Avogadro's number.

• Kinetic Theory of gases; derive p=1/3 rhobar(c^2) from the assumptions and applying Newton’s laws of motion. The average thermal velocity (rms value) crms=√3p/ρ; calculations for air, hydrogen and their comparison with common speeds. Effect of temperature and pressure on rms speed of gas molecules.
• [Note that pV=nRT the ideal gas equation cannot be derived from kinetic theory of ideal gas. Hence, neither can other gas laws; pV=nRT is an experimental result. Comparing this with p = 1/3 ρbar(c^2), from kinetic theory of gases, a kinetic interpretation of temperature can be obtained as explained in the next subunit].
• From kinetic theory for an ideal gas (obeying all the assumptions especially no intermolecular attraction and negligibly small size of molecules we get p = (1/3)ρ
• bar(c^2)or pV = (1/3)Mbar(c^2) (No further, as temperature is not a concept of kinetic theory). From experimentally obtained gas laws, we have the ideal gas equation (obeyed by some gases at low pressure and high temperature) pV = RT for one mole. Combining these two results (assuming they can be combined), RT=(1/3)Mbar(c^2)=(2/3).1/2Mbar(c^2)  =(2/3)K; Hence, kinetic energy of 1 mole of an ideal gas K=(3/2)RT. Average K for 1 molecule = K/N = (3/2) RT/N = (3/2) kT where k is Boltzmann’s constant. So, temperature T can be interpreted as a measure of the average kinetic energy of the molecules of a gas.
• Degrees of freedom and calculation of specific heat capacities for all types of gases. Concept of the law of equipartition of energy (derivation not required). Concept of mean free path and Avogadro’s number NA
1000 Oscillations and Waves

Oscillations: Periodic motion, time period, frequency, displacement as a function of time, periodic functions. Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring, restoring force and force constant; energy in S.H.M., Kinetic and potential energies; simple pendulum and derivation of expression for its time period.

Free, forced and damped oscillations (qualitative ideas only), resonance

• Simple harmonic motion. Periodic motion, time period T and frequency f, f=1/T; uniform circular motion and its projection on a diameter defines SHM; displacement, amplitude, phase and epoch, velocity, acceleration, time period; characteristics of SHM; Relation between linear simple harmonic motion and uniform circular motion. Differential equation of SHM, d2y/dt22y=0 from the nature of force acting F=-k y; solution y=A sin (ωt+Φ0) where ω2 = k/m; obtain expressions for velocity, acceleration, time period T and frequency f. Graphical representation of displacement, velocity and acceleration. Examples, simple pendulum, a mass m attached to a spring of spring constant k. Derivation of time period of simple harmonic motion of a simple pendulum, mass on a spring (horizontal and vertical oscillations) Kinetic and potential energy at a point in simple harmonic motion. Total energy E = U+K (potential +kinetic) is conserved. Draw graphs of U, K and E Verses y
• Free, forced and damped oscillations (qualitative treatment only). Resonance. Examples of damped oscillations (all oscillations are damped); graph of amplitude vs time for undamped and damped oscillations; damping force in addition to restoring force (-ky); forced oscillations, examples; action of an external periodic force, in addition to restoring force. Time period is changed to that of the external applied force, amplitude (A) varies with frequency (f) of the applied force and it is maximum when the frequency of the external applied force is equal to the natural frequency of the vibrating body. This is resonance; maximum energy transfer from one body to the other; bell graph of amplitude vs frequency of the applied force. Examples from mechanics, electricity and electronics (radio).

Waves: Wave motion, Transverse and longitudinal waves, speed of wave motion, displacement relation for a progressive wave, principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect.

• Transverse and longitudinal waves; characteristics of a harmonic wave; graphical representation of a harmonic wave. Distinction between transverse and longitudinal waves; examples; displacement, amplitude, time period, frequency, wavelength, derive v=f; graph of displacement with time/position, label time period/wavelength and amplitude, equation of a progressive harmonic (sinusoidal) wave, y = A sin (kx±ωt) where k is a propagation factor and equivalent equations.
• Production and propagation of sound as a wave motion; mechanical wave requires a medium; general formula for speed of sound (no derivation). Newton’s formula for speed of sound in air; experimental value; Laplace’s correction; variation of speed v with changes in pressure, density, humidity and temperature. Speed of sound in liquids and solids - brief introduction only. Concept of supersonic and ultrasonic waves
• Principle of superposition of waves; interference (simple ideas only); dependence of combined wave form, on the relative phase of the interfering waves; qualitative only - illustrate with wave representations. Beats (qualitative explanation only); number of beats produced per second = difference in the frequencies of the interfering waves. Standing waves or stationary waves; formation by two identical progressive waves travelling in opposite directions (e.g.,: along a string, in an air column - incident and reflected waves); obtain y= y1+y2= [2 ym sin (kx)] cos (ωt) using equations of the travelling waves; variation of the amplitude A=2 ymsin (kx) with location (x) of the particle; nodes and antinodes; compare standing waves with progressive waves.
• Laws of vibrations of a stretched string. Obtain equation for fundamental frequency f0=(1/2l) sqrt(T ; sonometer.
• Modes of vibration of strings and air columns (closed and open pipes); standing waves with nodes and antinodes; also in resonance with the periodic force exerted usually by a tuning fork; sketches of various modes of vibration; obtain expressions for fundamental frequency and various harmonics and overtones; mutual relations.
• Doppler effect for sound; obtain general expression for apparent frequency when both the source and listener are moving, given a f_L=f_r((v+-v_L)/(v+-v_r))which can be reduced to any one of the four special cases, by using proper sign.