《物理双语教学课件》Chapter 10 Waves 波动.docx

1、物理双语教学课件Chapter 10 Waves 波动Chapter 10 Waves 10.1 Types of Waves1. Mechanical waves: These waves are most familiar because we encounter them almost constantly; common examples include water waves, sound waves, and seismic waves. All these waves have certain central features: they are governed by Newt

2、ons laws, and they can exist only within a material medium, such as water, air, and rock.2. Electromagnetic waves: These waves are less familiar, but you use them constantly; common examples include visible and ultraviolet light, radio and television waves, microwaves, x-rays, and radar waves. These

3、 waves require no material medium to exist. Light waves from stars, for example, travel through the vacuum of space to reach us. All electromagnetic waves travel through a vacuum at the same speed c, given by c=299,792,458m/s.3. Matter waves: Although these waves are commonly used in modern technolo

4、gy, their type is probably very unfamiliar to you. Electrons, protons, and other fundamental particles, and even atoms and molecules, travel as waves. Because we commonly think of these things as constituting matter, these waves are called matter waves.4. Much of what we discuss in this chapter appl

5、ies to waves of all kinds. However, for specific examples we shall refer to mechanical waves.10.2 Transverse and Longitudinal Waves1. Transverse wave(1). A wave sent along a stretched, taut string is the simplest mechanical wave. If you give one end of a stretched string a single up-and-down jerk, a

6、 wave in the form of a single pulse travels along the string, as in the figure. This pulse and its motion can occur because the string is under tension. When you pull your end of the string upward, it begins to pull upward on the adjacent section of the string via tension between the two sections. A

7、s the adjacent section moves upward, it begins to pull the next section upward, and so on. Meanwhile, you have pulled down on your end of the string. So, as each section moves upward in turn, it begins to be pulled back downward by neighboring sections that already on the way down. The net result is

8、 that a distortion in the strings shape (the pulse) moves along the string at some velocity v. (2). If you move your hand up and down in continuous simple harmonic motion, a continuous wave travels along the string at velocity v. Because the motion of your hand is a sinusoidal function of time, the

9、wave has a sinusoidal shape at any given instant, as in the figure (b). That is, the wave has the shape of a sine curve or a cosine curve. (3). We consider here only an “ideal” string, in which no friction-like forces within cause the wave to die out as it travels along the string. In addition, we a

10、ssume that the string is so long that we need not consider a wave rebounding from the far end. (4). One way to study the waves of the figure is to monitor the waves form (shape of wave) as it moves to the right. Alternatively, we can monitor the motion of an element of the string as the element osci

11、llates up and down while the wave passes through it. We would find that the displacement of every such oscillating string element is perpendicular to the direction of travel of the wave, as indicated in the figure. This motion is said to be transverse, and the wave is said to be a transverse wave.2.

12、 Longitudinal wave:(1). The right figure shows how a sound wave can be produced by a piston in a long, air filled pipe. If you suddenly move the piston rightward and then leftward, you can send a pulse of sound along the pipe. The rightward motion of the piston moves the elements of air next to it r

13、ightward, changing the air pressure there. The increased air pressure then pushes rightward on the element of air somewhat farther along the pipe. Once they have moved rightward, the elements move back leftward. Thus the motion of the air and the change in air pressure travel rightward along the pip

14、e as a pulse. (2). If you push and pull on the piston in simple harmonic motion, as is being done in the figure, a sinusoidal wave travels along the pipe. Because the motion of the elements of air is parallel to the direction of the waves travel. The motion is said to be longitudinal wave. 3. Both a

15、 transverse wave and a longitudinal wave are said to be traveling waves because the wave travels from one point to another, as from one end of the string to the other end or from one end of the pipe to the other end. Note that it is the wave that moves between the two points and not the material (st

16、ring or air) through which the wave moves. 10.3 Wavelength and Frequency1. Introduction (1). To completely describe a wave on a string, we need a function that gives the shape of the wave. This means that we need a relation in the form, in which y is the transverse displacement of any string element

17、 as a function h of the time t and the position x of the element along the string. In general, a sinusoidal shape like the wave can be described with h being either a sine function or a cosine function; both give the same general shape for the wave. In this chapter we use the sine function. (2). For

18、 a sinusoidal wave, traveling toward increasing values of x, the transverse displacement y of a string element at position x at time is given by, here is the amplitude of the wave; the subscript m stands for maximum, because the amplitude is the magnitude of the maximum displacement of the string el

19、ement in either direction parallel to the y axis. The quantities k and are constants whose meanings are about to discuss. The quantity is called the phase of the wave.2. Wavelength and angular Wave Number(1). The figure shows how the transverse displacement y varies with position x at an instant, ar

20、bitrarily called t=0. That is, the figure is a “snapshot” of the wave at that instant. With t=0, the wave equation becomes. The Figure (a) is a plot of this equation; it shows the shape of the actual wave at time t=0. (2). The wavelength of a wave is the distance between repetitions of the wave shap

21、e. A typical wavelength is marked in figure (a). By definition, the displacement y is the same at both ends of this wavelength, that is, at and. Thus. (3). A sine function begins to repeat itself when its angle is increased by rad; so we have. We call k the angular wave number of the wave; its SI un

22、it is the radian per meter.3. Period, angular frequency, and frequency: (1). The figure (b) shows how the displacement y varies with time t at a fixed position, taken to be x=0. If you were to monitor the string, you would see that the single element of the string at that position moves up and down

23、in simple harmonic motion with x=0:. The figure (b) is a plot of this equation; it does not show the shape of the wave. (2). We define the period of oscillations T of a wave to be the time interval between repetitions of the motion of an oscillating string element. A typical period is marked in the

24、figure (b). We have. (3). This can be true only if. We call the angular frequency of the wave; its SI unit is the radian per second. (4). The frequency f of the wave is defined as 1/T and is related to the angular frequency by. This frequency f is a number of oscillations per unit time-made by a str

25、ing element as the wave moves through it, and f is usually measured in hertz or its multiples.10.4 The Speed of a Traveling wave1. The figure shows two snapshots of the wave taken a small time interval apart. The wave is traveling in the direction of increasing x, the entire wave pattern moving a di

26、stance in that direction during the interval. The ratio (or, in the differential limit, dx/dt) is the wave speed v. How can we find its value?2. As the wave moves, each point of the moving wave form retains its displacement y. For each such point, the argument of the sine function must be a constant

27、:.3. To find wave speed v, we take the derivative of the equation, get. The equation tells us that the wave speed is one wavelength per period.4. The wave equation describes a wave moving in the direction of increasing x. (1). We can find the equation of a wave traveling in the opposite direction by

28、 replacing t with t. (2). This corresponds to the condition. (3). Thus a wave traveling toward decreasing x is described by the equation. (4). Its velocity is.5. Consider now a wave of generalized shape, given by, where h represents any function, the sine function being one possibility. Our analysis

29、 above shows that all waves in which the variables x and t enter in the combination are traveling waves. Further more, all traveling waves must be the form above. Thus represents a possible traveling wave. The function , on the other hand, does not represent a traveling wave. 6. Wave Speed on a Stre

30、tched String (1). The speed of a wave is related to the waves wavelength and frequency, but it is set by the medium. If a wave is through a medium such as water, air, steel, or a stretched string, it must cause the particles of that medium to oscillate as it passes. For that happen, the medium must

31、possess both inertia and elasticity. These two properties determine how fast the wave can travel in the medium. And conversely, it should be possible to calculate the speed of the wave through the medium in terms of these properties. (2). We can derive the speed from Newtons second law as, where is

32、the linear density of the string, and the tension in the string. (3). The equation tells us that the speed of a wave along a stretched ideal string depends only on the characteristics of the string and not on the frequency of the wave.10.5 Energy and Power of a Traveling String Wave When we set up a wave on a stretched string, we provide energy for the motion of the string. As the wave moves away from us, it transports that energy as both kinetic energy and elastic potential energy. Let us consider each form in