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# Waves

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### Waves

1. 1. Waves:-Displacement: It is the change in position of an oscillating particle from its rest or meanposition in a particular direction. It is a vector.Amplitude: It is the magnitude of the maximum value of displacement. It is a scalar.Phase Difference: If two oscillations are in step with one another, they are said to be inphase with one another. Oscillations are said to be in antiphase if they are always moving inopposite directions. For example; if the crest of one wave falls with the trough of another,then they are said to be out of phase by 180 degrees.Period: The time taken to complete one oscillation.Frequency: The number of oscillations per unit time. It is measured in Hertz (Hz). 1 Hz isone cycle per second.Wavelength: It is the smallest distance between two points that are in phase with oneanother.(Wave) Speed: It is the speed with which crests of the wave move or the speed with whichenergy is transferred. It is NOT the speed with which particles in the wave move.The Transfer of Energy: The transfer of energy is due to a progressive wave, NOT astanding/stationary wave.Transverse Waves: A wave in which displacement of particles is perpendicular to thedirection of wave propagation, resulting in crests & troughs. E.g. light waves (the entireelectromagnetic spectrum)Longitudinal Waves: A wave in which displacement of particles is parallel to the direction ofwave propagation, resulting in compressions & rarefactions. E.g. sound wavesElectromagnetic Waves: These are transverse waves. The displacement in the case ofelectromagnetic waves is a variation in the electric & magnetic fields perpendicular to eachother.Polarisation: As a result of the transverse nature of vibrations, transverse waves have anadditional property that is not possessed by longitudinal waves. The movement of particlesin transverse mechanical waves is at right angles to the direction of wave propagation. This,however, still leaves many possibilities for the direction of the particle in 3D. Frequently,oscillations take place in a transverse wave in many different directions, & the wave is said
2. 2. to be unpolarised. If the oscillation does take place in only one direction, however, the waveis then said to be polarized in that direction. That wave is then known as a plane-polarisedwave.Stationary Waves: A stationary wave is produced because of superposition of two waves ofsimilar wavelength & amplitude, but travelling in opposite directions. A characteristic of astationary wave is that there are some parts of the wave where the amplitude is always zero.The points are known as nodes. Halfway between the nodes, the amplitude is at itsmaximum, & these points are called antinodes. Energy is NOT transferred in standingwaves.Diffraction: The spreading of waves near an obstacle is called diffraction. If the width of theopening is comparable with a single wavelength, the magnitude of diffraction is large ascompared with say, if the width of the opening was five wavelengths.Diffraction Grating: It is a series of narrow parallel slits. If parallel monochromatic lightwaves approach a series of narrow slits close to one another, the waves from each slit arespread out over 180 degrees after passing the slits. It is the ability of a diffraction grating togive a dark background, where the intensity is near zero, that makes it useful for examiningspectra.Principle of Superposition Of Waves: When two waves of the same type with similarfrequency & speed are in phase with each other, their total amplitude on joiningtogether/adding together is the sum of their individual amplitudes.Interference: When two waves superimpose, they cause interference. When the crests ofboth waves fall on each other, constructive interference is achieved & the displacement ofparticles is at its maximum value. If the crest of one wave falls on the trough of the other,destructive interference takes place & the displacement of particles is at its minimum value,or zero.Coherence: If monochromatic light is used, only one wavelength is present, as compared toif white light was used. Since speed & frequency are the same, all imperfections within thewave occur simultaneously for both sources of the monochromatic light. Two wavesmaintaining a constant phase difference are said to be coherent.Fringe Width/Separation: The separation between one bright fringe & the next brightfringe.Conditions for Observing Two-Source Interference:· The two waves should be of the same type. (Both transverse or longitudinal).· They should almost similar wavelength or frequency.
3. 3. · They should arrive at a point at the same time (superimposed).· They should maintain a constant phase difference. (Coherent sources are required).Electricity:-Electric Field: It is the modified area or region around a charged object in which it can applyan electrostatic force of attraction or repulsion on a test charge. Electric field strength isforce per unit positive charge.Electric Current: It is the amount of charge flowing through a circuit per unit time or It isthe rate of flow of charged particles.Ampere: If a charge of 1 Coulomb passes through an electrical component per second, thenthe current maintained is 1 Ampere.Potential Difference: The P.D across an electrical component is the energy converted fromelectrical to other forms of energy when unit charge passes through it.Volt: One volt is the P.D between two points in a circuit in which one joule of energy isconverted when one coulomb of charge passes from one point to the other.Resistance: The ratio of P.D to the current for an electrical component at a particular time isknown as its resistance.Ohm: A resistor has a resistance of one ohm if a P.D of one volt is to be maintained, to allowa passage of one ampere of current.Resistivity: The resistivity of a wire of a particular material is its resistance for unit length.Coulomb: If a current of one ampere (6.25x1018 electrons) passes through a conductor, thenthe charge flowed is one Coulomb or It is the amount of charge required to maintain acurrent of one ampere in a conductor.Ohm’s Law: The current through a metallic conductor is proportional to the P.D across itprovided that its temperature remains constant.Thermistor (NTC): A specific type of resistor, in which, as temperature increases, themagnitude of the resistor’s resistance decreases, & vice versa.Electromotive Force: The e.m.f of any source of electrical energy is the energy convertedinto electrical energy per unit charge supplied. It has the same unit as P.D; the volt.
4. 4. E.m.f & P.D: While e.m.f refers to the amount of energy converted into electrical energy perunit charge supplied, P.D refers to the amount of electrical energy converted into otherforms of energy per unit charge supplied. The e.m.f of a source is equal to the potentialdifference across its terminals as the current approaches zero.Effect of Internal Resistance on P.D & Output Power: The higher the internal resistance ofthe battery/cell, the lower the terminal P.D, & hence, the lower the output power as well.This is due to the equation V = E – IrPotentiometer: When a potential divider arrangement is used to compare e.m.fs of twosources, it is known a potentiometer.Kirchhoff’s First Law: The algebraic sum of the currents at a junction is zero. In otherwords, charge cannot be created or destroyed.Kirchhoff’s Second Law: Around any closed loop in a circuit, the algebraic sum of the e.m.fsis equal to the algebraic sum of the P.Ds. In other words, each & every point in a stableelectrical circuit has a particular value of potential. Any gains in electrical energy of a chargemust be balanced by corresponding losses of energy.Kirchhoff’s First & Second Laws are in correspondence & actually are an appreciation of theLaw of Conservation of Charge & the Law of Conservation of Energy respectively.