1、Chapter 18Wave Motion18-1 Mechanical wavesIn this chapter,we consider only mechanical waves,such as sound waves,water waves,and the waves transmitting in a guitars strings.Elastic mediums are needed for the travel of mechanical waves.Mechanical waves can appear when an initial disturbance is made to
2、 the mediums.On a microscopic level,the forces between atoms in the mediums are responsible for the propagation of the waves.The particles of the medium do not experience any net displacement in the direction of the wave-as the wave passes,the particles simply move back and forth through small dista
3、nce about their equilibrium position.What is a wave?It is the process of propagating oscillation in space.What are transmitted by a wave?Energy,momentum,phase,but the particles are not.18-2 Types of wavesWaves can be classified according to their properties as following.1.According to direction of p
4、article motion(a)“Transverse waves(横波)”:If the motion of the particle is perpendicular to the direction of propagation of the waves itself.(b)“Longitudinal wave(纵波)”:If the motion of the particle is parallel to the direction of propagation of the waves.See动画库波动与光学夹2-01波的产生 2 3 2.According to number
5、of dimensions1-D Waves moving along the string or spring2-D Surface waves or ripple on water3-D Waves traveling radially outward from a small source,such as sound waves and light waves.3 According to periodicitypulse waves or periodic wave.The simplest periodic wave is a“simple harmonic wave in whic
6、h each particle undergoes simple harmonic motion.yxoThe simplest periodic waveOther kinds of periodic waves:Square waveTriangle wavemodulated waveSawtoothed wave4.According to shape of wavefronts(a)The definitions of wave surface(波面或同相面)and wavefront(波前或波阵面)?See动画库波动与光学夹2-02波的描述 1 (b)The definition
7、of a ray(波线):A line normal to thewavefronts,indicating the direction of motion of the waves.Wavefronts are always direction of RayPlane wave:The wavefronts are planes,and the rays are parallel straight lines.Spherical wave:The wavefronts are spherical,and the rays are radial lines leaving the point
8、source in all directions.Two different types of wavefronts:Plane wavesSpherical wavesRay(波线波线)Wave surface(波面波面)Wavefront(波前波前)*Spherical wavePlane wave波前波前波面波面ray5.Waves in different fields in physicssound waveswater wavesearthquake waveslight waveselectromagnetic wavesgravitational wavesmatter wav
9、eslattice waves18-3 Traveling waves(行波)All the waves would travel or propagate,why heresay traveling waves?(with respect to standing wave(驻波)Definition of traveling waves:The waves formed and traveling in an openmedium system.Description of traveling wavesWe use a 1-D simple harmonic,transverse,plan
10、ewave as an exampleMathematics expressionsThe vibration displacement y as a function of t and x.The difference between vibration and wave motion:Vibration y(t):displacement as a function of timeWave y(x,t):displacement as a function of bothtime and distance)2sin()0,(xyxym=Fig 18-6vtyxt=0t=tWhat we w
11、ant to know:=),(txy)(2sin(vtxym1.Equation of a sine waveIf there is initial phase constant in the sinusoidal waves,the general equation of the wave at time t is:)(2sin(),(=vtxytxym(18-16)Several important concepts about waves:1)The period T of the wave is the time necessary forpoint at any particula
12、r x coordinate to undergo one complete cycle of transverse motion.During this time T,the wave travels a distance that must correspond to one wavelength .vT2)The wavelength :the length of a complete wave shape.3)The frequency of the wave:Tf1=4)The wave number:2=k5)The angular frequency:fT22=(18-16)si
13、n(),(=tkxytxymNote that:speed of the waveThe equation of a sine wave traveling in direction isx+)sin(),(=tkxytxymThe equation of a sine wave traveling in the direction is x)sin(),(+=tkxytxym(18-11)(18-12)kfv=(18-13)(18-16)2.Transverse velocity of a particlevNote that is the speed of wave transmittin
14、g.What is the velocity of particle oscillating?-It is called transverse velocity of a particle fortransverse wave)cos()sin(),(tkxytkxyttytxummy=Transverse velocity:Tansverse acceleration:ytkxydtydtxamy2222)sin(),(=(18-14)(18-15)3.Phase and phase constant)sin(),(=tkxytxym)(tkxIf the equation of the w
15、ave is:Phasephase constantEq(18-16)can be written in two equivalent forms:(18-17a)(18-17b)(sin),(tkxkytxym=)(sin),(+=tkxytxym(18-16)In y-x,wave A is ahead of wave B by a distance/kIn y-t,wave A is ahead of wave B by a time/(a)xkB Ayy=ymsin(kx t)Two waves A and B:y=ymsin(kx t)wave Awave B (b)tFig 18-
16、7yAB)(sin),(tkxkytxym=)(sin),(+=tkxytxymleadlagSample problem 18-1A transverse sinusoidal wave is generated at one end of a long horizontal string by a bar that movesthe end up and down through a distance of 1.30cm.The motion is repeated regularly 125 times per second(a)If the distance between adjacent wave crests is 15.6 cm,find the amplitude,frequency,speed,and wavelength of the wave.(b)Assuming the wave moves in the+x direction and that at t=0,the element of the string at x=0 is at its equili
