重邮大学物理英文版PPT (13)

1、The net vibration,Review,Superposition of vibration,Chapter 2,Mechanical waves,Waves: a disturbance travels away from its source,Water waves, sound waves, radio waves, X-rays,Waves,Mechanical Waves,The disturbance is propagating through a medium,electromagnetic Waves,Do not need a medium,Waves,Trans

2、verse Waves,The medium oscillates perpendicular to the direction the wave is moving,Longitudinal Waves,Water wave,The medium oscillates in the same direction as the wave is moving,sound wave,Mechanical Waves,The propagation of a disturbance in a medium,The conditions all the mechanical waves require

3、,1) Some source of disturbance,2) A medium that can be disturbed,3) Some physical mechanism through which particles can influence one another,The essence of mechanical waves,The disturbance is transferred through space, but the matter does not,The propagation of the disturbance also means a transfer

4、 of energy,Waves on a String,11,2-1 harmonic waves,The characteristic of harmonic waves,Every medium element oscillates around the equilibrium position in simple harmonic motion, but the wave propagates away from the source of disturbance,The propagation of simple harmonic motion in space,2)The phas

5、e of the particle which oscillates later is smaller,medium,disturbance,v,18,y(x,t) = A cos(wt kx,A = amplitude,= angular frequency,k = wave number = 2,harmonic wave function,Assuming: initial phase is zero at x=0 and t=0,Generally,The transverse displacement is not zero at x=0 and t=0,Phase constant

6、,Can be determined from the initial conditions,Simple harmonic vibration function,The vibration y as a function of time t,The harmonic wave function,The wave function y(x, t) represents the y coordinate of any point P located at position x at any time t,Two variables x and t,If t is fixed, the wave

7、function y as a function of x, called waveform, defines a curve representing the actual geometric shape of the pulse at that time,Amplitude and Wavelength,Wavelength : The distance between identical points on the wave,Amplitude A: The maximum displacement of a point on the wave,19,Period and Velocit

8、y,21,Wave Properties,The speed of a wave is a constant that depends only on the medium, not on amplitude, wavelength or period (similar to SHM,and T are related,= u T or = 2 u /,or = u / f,Example 2-1-1,Suppose the harmonic vibration function of origin at t,Find: the harmonic wave function of point

9、P at t,Solution: the time for the vibration to arrive point P is,The vibration at point P at t is identical with that of point O at t-t,Then we have the wave function of point P,Example 1-1-2,Suppose the harmonic vibration function of origin at t,Find: the harmonic wave function of point P at t,The

10、vibration at point P at t is identical with that of point O at t+t,Therefore, the harmonic wave function can be written as,Or,If the wave travels left, use x substitute x,The parameters A， u of a certain planar cosine wave are known. Calculating t=0 from the moment of the following figure, 1)write t

11、he wave function taking O and P as the origin respectively. 2) Find the magnitude and direction of the speed at x1= / 8 and x2= 3/ 8 when t=0,Example 2-1-3,Solution: 1) taking O as the origin,The vibration function of O is,When t=0,then,The velocity of x=0 at t=0,The simple harmonic vibration curve,

12、The velocity at a certain time,is the slope of the tangent line of that point,The harmonic wave curve (displacement as a function of x,t=t1,t=t2, t2t1,If the slope of a certain point of the curve y(x) 0, the velocity at this point 0 (the wave travels right wards,Solution: 1) taking O as the origin,T

13、he vibration function of O is,When t=0,then,The velocity of x=0 at t=0,thus,Therefore, the vibration function of O is,The wave function of x taking O as origin is,1) taking P as the origin,The vibration function of P is,When t=0,then,Anyone is Ok, we choose,The wave function of x taking P as origin

14、is,The wave function of x taking O as origin is,The wave function of x taking P as origin is,We must identify the origin point clearly,The phase constants are different if we take various original points,2) Find the magnitude and direction of the speed at x1= / 8 and x2= 3/ 8 when t=0,The velocity a

15、t x point,Because the vibration is,The velocity at x point at t moment,Take x=/8, t=0 into the above equation,Along the negative y axis,Take x=3/8, t=0 into the above equation,Along the positive y axis,2-2 wave speed / phase speed u,The speed of a wave is a constant that depends only on the medium,a

16、nd T are related,Note: the speed of the wave u is different from the vibration velocity of a certain medium element v,The speed of a wave is a constant that depends only on the medium,A) Wave propagating in liquid, gas/ fluid,B : bulk elastic modulus,: the density of the medium,B) Wave propagating i

17、n solid,1) Transverse wave,G : shear elastic modulus,2) longitudinal wave,Y : Young modulus,2-3 energy of harmonic waves,Mechanical wave: The disturbance is propagating through a medium,disturbance,Vibration state,phase,energy,Energy of traveling harmonic waves,The wave function,The waveform (at t=t

18、1,Segment AB in the medium,The mass of AB,the mass density of the medium,The kinetic energy of AB,The potential energy of AB,T: tension,The magnitude and phase of kinetic energy and potential energy are identical at any time,Note: the energy difference between wave and vibration,waveform,Maximum deformation,Max