西南交大：《大学物理》（双语版）Chapter 12 Waves

UNIVERSITY PHYSICS I CHAPTER 12 Waves Chapter 12 Waves wave motion is the most universal physical phenomenon, we discover the wave motion all around us Mechanical waves -acoustic wave, water wave Electromagnetic waves--radio light wave Matter waves-electron wave Wave is a propagating disturbance that transfers energy, momentum and information as its own characteristic speed from one region of space to another We will concentrate to the mechanical waves

1 Chapter 12 Waves Wave motion is the most universal physical phenomenon, we discover the wave motion all around us. Mechanical waves—acoustic wave, water wave Electromagnetic waves—radio, light wave Matter waves—electron wave We will concentrate to the mechanical waves. Wave is a propagating disturbance that transfers energy, momentum and information as its own characteristic speed from one region of space to another

$12.1 mechanical waves 1. What is mechanical waves? Source of wave-a disturbance(oscillation) Medium-for propagation of waves 2. Classification of mechanical waves According to the direction of particle motion Longitudinal waves: waves whose oscillation or jiggling is along the line the wave propagates. 数的家 $12.1 mechanical waves Transverse waves: the waves whose oscillation or jiggling is perpendicular to the line along which the waves propagates.> Plane of polarization--the plane in which the jiggling f a transverse waves disturbance occurs Pulse wave. Periodic train of waves:

2 §12.1 mechanical waves 1. What is mechanical waves? Source of wave—a disturbance(oscillation) Medium—for propagation of waves Longitudinal waves: waves whose oscillation or jiggling is along the line the wave propagates. According to the direction of particle motion 2. Classification of mechanical waves Plane of polarization-- the plane in which the jiggling of a transverse waves disturbance occurs. Pulse wave: Periodic train of waves: §12.1 mechanical waves Transverse waves: the waves whose oscillation or jiggling is perpendicular to the line along which the waves propagates

$12.1 mechanical waves Wavefronts-the surfaces on them all the points are in the same state of motion Wave ray--the direction which are perpendicular to the wavefronts or parallel to the velocity of the waves Ray Ra $12.1 mechanical waves According to the shape of the wavefronts Plane waves: the wavefronts are plane Cylindrical wave: the wavefronts are cylindrical Spherical wave: the wavefronts are spherical

3 Wavefronts—the surfaces on them all the points are in the same state of motion. Wave ray—the direction which are perpendicular to the wavefronts or parallel to the velocity of the waves §12.1 mechanical waves According to the shape of the wavefronts Plane waves: the wavefronts are plane Cylindrical wave: the wavefronts are cylindrical Spherical wave: the wavefronts are spherical §12.1 mechanical waves

$12.1 mechanical waves Seismic waves =150m/s earthquakes produce both longitudinal and transverse waves →d=7△ Sand scorpion located its prey by using longitudinal and tuc pulses transverse waves. Transverse Beetle th 812.2 one-dimensional waves and the equation of waves 1. Wavefunction of one-dimensional waves moving at constant velocity y(x,0)=y(x) y(x,)=y(x) =Y(r-vt) y(x,t)=平(x’) Y(x+v)

4 Seismic waves— earthquakes produce both longitudinal and transverse waves Sand scorpion— located its prey by using longitudinal and transverse waves. §12.1 mechanical waves = 150m/s = 50m/s d t v d v d t l t ∆ = − ⇒ = 75∆ §12.2 one-dimensional waves and the equation of waves 1. Wavefunction of one-dimensional waves moving at constant velocity x y o x(x´) y y´ o o´ x • • vt x′ P P y(x,0) =Ψ(x) ( ) ( , ) ( ) Ψ x vt y x t Ψ x = − = ′ v → −v ( ) ( , ) ( ) Ψ x vt y x t Ψ x = + = ′

12.2 one-dimensional waves and the equation of waves yP(x,0)=yp(x,t) r-vt= constant phase d v=0→p= dt d x(x) Phase speed 812.2 one-dimensional waves and the equation of waves 2. The classical wave equation y(x,t)=平(x-v)=(u) a ay au a 0y202y ax au ax au at a 02y、au or au au a a-p ap 0=0 2=(,o、an_n0 at au at ay a v au au at u

5 x y o x(x´) y y´ o o´ x • • vt x′ P P y (x,0) y (x,t) P = P x − vt = constant phase t x v v t x d d 0 d d − = ⇒ = Phase speed §12.2 one-dimensional waves and the equation of waves 2. The classical wave equation u x vt y x t Ψ x vt Ψ u = − ( , ) = ( − ) = ( ) 2 2 2 2 ( ) u Ψ x u u Ψ x u Ψ u Ψ x u u Ψ x Ψ ∂ ∂ = ∂ ∂ ∂ ∂ ∂ ∂ = ∂ ∂ ∂ ∂ = ∂ ∂ ∂ ∂ = ∂ ∂ 2 2 2 2 2 ( ) u Ψ v t u u Ψ v t u Ψ u Ψ v t u u Ψ t Ψ ∂ ∂ = ∂ ∂ ∂ ∂ − ∂ ∂ = ∂ ∂ ∂ ∂ = − ∂ ∂ ∂ ∂ = ∂ ∂ 2 2 2 2 2 x Ψ v t Ψ ∂ ∂ = ∂ ∂ 0 1 2 2 2 2 2 = ∂ ∂ − ∂ ∂ t Ψ x v Ψ or §12.2 one-dimensional waves and the equation of waves

§122。ne- dimensional waves and the equation of waves 3. Periodic waves (a)Space period Y(, t A snapshot at some instant to (b) Time period (x,D) An oscillation at any given position o I 812.2 one-dimensional waves and the equation of waves n one time period, some oscillatory state propagate one space period. T Phase speed:v=y=元v T 6

6 3. Periodic waves x ( , ) 0 Ψ x t λ o λ (a) Space period A snapshot at some instant t0 o t ( , ) 0 Ψ x t T T (b) Time period An oscillation at any given position x0 §12.2 one-dimensional waves and the equation of waves In one time period, some oscillatory state propagate one space period. Phase speed: λ ν λ = = ⋅ T v λ T §12.2 one-dimensional waves and the equation of waves

§122。ne- dimensional waves and the equation of waves (c Traveling wave y(x,) A=vT =νT 4. Sinusoidal (harmonic)waves Y(x, t)=Acos k(r-v) Y(x, t) 812.2 one-dimensional waves and the equation of waves 4. The physical meaning of the harmonic waves Model: One-dimensional harmonic waves If the oscillatory equation at point o is Yo=Acos(@t +o)--harmonic motion y=平(x,t)=?

7 x Ψ(x,t) v r o λ = vT v∆t (c) Traveling wave ν = λ = vT v =νλ T 1 4. Sinusoidal (harmonic) waves Ψ(x,t) = Acos[k(x − vt)] x Ψ(x,t) v r o λ §12.2 one-dimensional waves and the equation of waves 4. The physical meaning of the harmonic waves Model: One-dimensional harmonic waves x v r o If the oscillatory equation at point o is cos( ) Ψ0 = A ωt + φ Ψ = Ψ( x,t) = ? --harmonic motion §12.2 one-dimensional waves and the equation of waves

§122。ne- dimensional waves and the equation of waves Choose a ray of wave as x axis, construct a one-dimensional coordinate system. O is the origin, v is the velocity along the tx direction. Method 1 P(r) ifY0=Acos(ot+φ) The propagating time of the、△ state from point o to point P(c) The phase of point P(r)at instant t is the same as the point o at instant t-4t 812.2 one-dimensional waves and the equation of waves therefore Yn(x,)=0(0,t-△)=Acoo(t-)+外 (x,D)= Acosta(-1)+y(1) Method 2: L P The phase difference between two points of space interval of n is 2T. The phase at point P lag .2 relative to point o 8

8 Method 1 if cos( ) Ψ0 = A ωt + φ′ v O P(x) x The propagating time of the state from point o to point P(x) v x ∆t = Choose a ray of wave as x axis, construct a one-dimensional coordinate system. O is the origin, v is the velocity along the +x direction. The phase of point P(x) at instant t is the same as the point o at instant t-∆t. §12.2 one-dimensional waves and the equation of waves ( , ) = cos[ω( − t) +φ] v x Ψ x t A (1) ( , ) (0, ) 0 Ψ x t Ψ t t p = − ∆ = cos[ω( − ) +φ′] v x A t therefore u O P(x) x Method 2: The phase at point P lag relative to point o π λ ⋅ 2 x The phase difference between two points of space interval of λ is 2π. §12.2 one-dimensional waves and the equation of waves

§122。ne- dimensional waves and the equation of waves p(r,t=AcoS(at -2.2z) x or平(x,t)=Ac0s(…·2丌-o+φ)(2) Y(x, t)=Acos o(--t)+9](1) Due to见 Equations(1)and (2)is identical. 812.2 one-dimensional waves and the equation of waves y(x,t)= A cos a(-t)+小 A cos(2-at+y A coS 2( )+小 见T A cos( lx -at+o) Acos{k(x-v)+小 where元=wTa= 2兀k= T 2λ

9 Equations (1) and (2) is identical. ( , ) cos( 2π ) λ = ω + φ′ − ⋅ x Ψ x t A t p ( , ) cos( 2π ω φ ) λ = ⋅ − t + x or Ψ x t A (2) ω π λ 2 Due to = vT = v §12.2 one-dimensional waves and the equation of waves ( , ) = cos[ω( − t) +φ] (1) v x Ψ x t A λ π π λ ω 2 2 = = k = T where vT §12.2 one-dimensional waves and the equation of waves ( , ) = cos[ω( − t) + φ ] v x Ψ x t A cos( 2 ω φ ) λ = π − t + x A cos[ 2 ( ) φ ] λ = π − + T x t A = LL = Acos[ k( x − vt ) + φ ] = Acos( kx −ωt + φ )

812.2 one-dimensional waves and the equation L of waves 6. The comparison of graphs of oscillation and waveform T, A, o, the moving direction of point (b) The graphs of waveform u AFoAZ A,a, determine o from the graph of waveform at t=0, the moving direction of point 812.2 one-dimensional waves and the equation of waves Example: figure depicts the waveform of a traveling sinusoidal wave at instants t=0 S, find(a) the oscillatory equation of point o; (b) the wavefunction P(x, t); (c) the oscillatory equation of point P;(d) the moving directions of points a and b y(x,0) v=0.08m/s 0.04 b 10

10 §12.2 one-dimensional waves and the equation of waves 6. The comparison of graphs of oscillation and waveform T, A, φ, the moving direction of point (a) The graphs of oscillation A, λ, determine φ from the graph of waveform at t=0, the moving direction of point (b) The graphs of waveform • • a b x(m) 0.04 Ψ(x,0) o 0.2 P v = 0.08m/s Example: figure depicts the waveform of a traveling sinusoidal wave at instants t=0 s, find (a) the oscillatory equation of point o; (b) the wavefunction ;(c) the oscillatory equation of point P; (d) the moving directions of points a and b. Ψ(x,t) §12.2 one-dimensional waves and the equation of waves