Chapter 10 Wave Motion Chapter 10 Wave Motion

Chapter 10 Wave Motion §1. Several Concepts of Mechanical WaveSeveral Concepts of Mechanical Wave §2. Wave Function of Simple Harmonic WaveWave Function of Simple Harmonic Wave §3. Energy in Wave Motion, Energy Flux DensityEnergy in Wave Motion, Energy Flux Density §4. Huygens Principle, Diffraction and Interference of WavesHuygens Principle, Diffraction and Interference of Waves §5. Standing WavesStanding Waves §6. Doppler EffectDoppler Effect §7. Plane Electromagnetic WavesPlane Electromagnetic Waves

§1. Several Concepts of Mechanical Wave 1. The formation of mechanical waveThe formation of mechanical wave 2. Transverse wave and longitudinal waveTransverse wave and longitudinal wave 3. Wavelength, wave period and frequency, wave speedWavelength, wave period and frequency, wave speed 4. Wave line, wave surface, wave frontWave line, wave surface, wave front

Elastic medium which can propagate mechanical oscillation 2 Medium An object which is oscillating mechanically 1 Wave source What are propagated is the oscillation states, while the mass points do not flow away. Notice 1. The formation of mechanical wave

1 Transverse wave 2. Transverse wave and longitudinal wave Characteristics: The oscillation directions of mass points are perpendicular to the direction of travel of the wave.

2 Longitudinal wave Characteristics: The oscillation directions of mass points are parallel to the direction of travel of the wave.

3 Complex wave Characteristics: Any complex wave motions can be viewed as a superposition of transverse waves or longitudinal waves.

O y A A  1 Wavelength 3. Wavelength, wave period and frequency, wave speed

2 Period T 3 Frequency The period (or frequency) of wave is equal to the oscillation period (or frequency) of the wave source.

The magnitude of the wave velocity depends on the nature of media. 4 Wave velocity

In solid In liquid and gas (transverse wave) (longitudinal wave)

The curved surface by connecting the points with the same phase on the different wave lines 1 Wave line 2 Wave surface The lines drawn with arrows along the direction of wave propagation At one instant, the curved surface connected by every point with the original state of wave source 4. Wave line, wave surface, wave front Wave front In isotropic medium, wave line is perpendicular to wave surface.

Classification (2) Spherical wave (1) Plane wave

1. Wave function of simple harmonic waveWave function of simple harmonic wave 2. The physical meaning of wave functionThe physical meaning of wave function §2. Wave Function of Simple Harmonic Wave

In the homogeneous and non-absorbing medium as the wave source is in simple harmonic motion, the wave formed is called plane simple harmonic wave. 1. Wave function of simple harmonic wave

A mass point is in simple harmonic motion at origin O. Its motion equation is: O P x

At time t, the displacement of point P is: This is the function of plane simple harmonic wave spreading along the positive direction of Ox axis, and it is also called the wave equation of plane simple harmonic wave.

The equation can be written in the following three commonly used forms:

then if 1 When x is fixed The equation gives the displacement of the mass point, which is x away from origin O, at different time. 2. The physical meaning of wave function

The curve of displacement versus time for a simple harmonic motion of every mass point on wave line

then 2 When t is fixed The equation represents the distribution of displacement of every mass point at the given time. if y o x x1x1 x2x2

The equation expresses the overall situation of displacement varying with time of all mass points. 3 When both x and t are in variation O waveform at time t waveform at time t+ x

O P x 4 If the plane simple harmonic wave travels along the negative x-direction:

§3. Energy in Wave Motion, Energy Flux Density 1. The propagation of wave energyThe propagation of wave energy 2. Energy flux and energy flux densityEnergy flux and energy flux density

1 Wave energy 1. The propagation of wave energy Take the longitudinal wave in a rod as an example: Kinetic energy of oscillation: x O x O

Elastic potential energy: Total energy of this volume element:

They all reach the maximum at the equilibrium position, whereas they are all zero at the maximum displacement. 2) The mechanical energy in each volume element is not constant. Discussion 1) have the same phase. 3) Wave motion is a mode of dissemination of energy.

Energy density : Average density of energy : x O x O

Energy flux: udtudt S 2. Energy flux and energy flux density Average energy flux:

Energy flux density ： udtudt S

§4. Huygens Principle, Diffraction and Interference of Waves 1. Huygens principleHuygens principle 2. The diffraction of wavesThe diffraction of waves 3. The interference of wavesThe interference of waves

spherical wave plane wave The every point of a wave front in the medium may be considered the sources of emitting secondary wavelets that spread out in all directions, and at any later time the envelope of these secondary wavelets is the new wave front. O 1. Huygens principle

wave diffraction diffraction phenomena formed by water When wave strikes a barrier in the process of spreading, it can round the edge of the barrier and go on spreading in the shade area of the barrier. 2. The diffraction of waves

1 Superposition principle of waves The waves will keep their own properties without any change after they meet, and keep traveling in their original directions as if they had never met each other. The oscillation at any point in the area where the waves meet is the vector sum of their separate oscillation displacements produced by every wave existing at the same point independently. 3. The interference of waves

If there are two waves with the same frequency, the parallel oscillation direction, the same phase or the invariant phase difference, when they meet the oscillations of some areas are always strengthened and the oscillations of some other areas are always weakened. 2 The wave’s interference

Oscillations of wave sources: Oscillations at point P: The conditions for constructive and destructive interference *

constant *

when “Phase Difference” conditions for interference Discussion

Phase difference The difference of wave paths then if constructive destructive

when “Wave Path Difference” conditions for interference

§5. Standing Waves 1. Formation of standing wavesFormation of standing waves 2. Equation of standing wavesEquation of standing waves 3. Phase jumpPhase jump 4. Energy in standing wavesEnergy in standing waves 5. Normal modes of oscillationNormal modes of oscillation

1 Phenomena 1. Formation of standing waves 2 Conditions

3 Formation of standing waves The standing wave is a particular interference phenomenon that produced by two coherent waves with the same amplitude, frequency and wave speed traveling in the opposite direction along the same straight line.

the positive x-direction the negative x-direction 2. Equation of standing waves

Equation of standing waves 1 0 (1) Amplitude,, only depends on x Discussion

antinodes b when a when nodes

Distance between two adjacent node and antinode Distance between two adjacent nodes Conclusions x y node antinode some points remain still all the time; while the amplitudes of some other points are the maximum.

( 2 ) Phase Conclusion 1 Between two adjacent nodes, the phase of every point is the same. x y

Conclusion 2 The phases of both sides of one node are opposite. x y

At any time, the standing wave has a certain waveform, but it does not appear to be moving in either direction along string. Every point oscillates in the vicinity of its own equilibrium position with the certain amplitude. x y

denser medium thinner medium thinner medium denser medium 3. Phase jump

denser medium thinner medium

When the wave shoots from the denser medium to the thinner medium, the wave node forms at the reflected end. This indicates the incident and reflected waves are exactly out of phase with each other all the time. It means the wave path difference with half of the wavelength is produced, which is called the phase jumping or half-wave loss.

AB C node antinode maximum displacement equilibrium position 4. Energy in standing waves The standing wave does not spread energy.

——The normal mode of the string oscillation For a string of which both ends are fixed, the wavelength and the string length should satisfy the following relationship:, 5. Normal modes of oscillation

The normal mode of oscillation on a string with two fixed ends:

The normal mode of oscillation of an air column in a glass tube with one opening end and one closed end:

§6. Doppler Effect 1. Observer moving with velocity v 0 relative to medium while wave source is at restObserver moving with velocity v 0 relative to medium while wave source is at rest 2. Wave source moving with velocity v s relative to medium while observer is at restWave source moving with velocity v s relative to medium while observer is at rest 3. Wave source and observer moving simultaneously relative to mediumWave source and observer moving simultaneously relative to medium

Frequency of wave source ——the number of complete oscillations of wave source occurring per unit time Frequency received by observer ——the number of oscillations that observer receives per unit time Frequency of wave —— the number of oscillations of mass point in medium per unit time

P 1. Observer moving with velocity v 0 relative to medium while wave source is at rest

Frequency received by observer Observer moving towards wave source Observer moving away from wave source

2. Wave source moving with velocity v s relative to medium while observer is at rest

A

A Frequency received by observer Wave source moving towards observer Wave source moving away from observer

observer moving towards wave source + away from - wave source moving towards observer – away from + As long as the two approach each other, the received frequency is higher than that of original wave source; and if the two are apart from each other, the received frequency is lower than that of original wave source. 3. Wave source and observer moving simultaneously relative to medium

If wave source and observer do not move down their connection line:

§7. Plane Electromagnetic Waves 1. Generation and propagation of electromagnetic wavesGeneration and propagation of electromagnetic waves 2. Characteristics of plane electromagnetic wavesCharacteristics of plane electromagnetic waves 3. Energy in electromagnetic wavesEnergy in electromagnetic waves 4. The electromagnetic spectrumThe electromagnetic spectrum

+ Electromagnetic waves are formed by the propagation of alternating electromagnetic fields in space. - + oscillation dipolar Generation and propagation of electromagnetic waves

Electric filed for different moments in the vicinity of oscillating electric dipole Electric and magnetic fields in the vicinity of oscillating electric dipole

pole axis propagation direction

Plane electromagnetic waves

2. Characteristics of plane electromagnetic waves

(1) Electromagnetic wave is transverse wave:, (2) and are in phase. (3) Values of and are in proportion: (4) The propagation speed of electromagnetic wave in vacuum equals the speed of light in vacuum:

The energy propagating in the form of electromagnetic waves is called the radiant energy. Energy flux density of electromagnetic waves  Energy density of electromagnetic field  Vector of the energy flux density of electromagnetic wave (Poynting’s vector) 3. Energy in electromagnetic waves and

Average of energy flux density of the plane electromagnetic wave Average radiation power of oscillating dipole

760 nm 400 nm visible light Electromagnetic Spectrum infrared ultraviolet -ray X-ray long-wavelength radio frequency / wavelength / Short-wavelength radio 4. The electromagnetic spectrum

radio waves visible light infrared ray ultraviolet ray X-rays -rays