1. Examples: Wave motion is generating, when disturbance is generating in a wave source and the disturbance is propagating in time and in space.

Transcription

1 Wave motion

2 1. Examples: Wave motion can be observed when a water surface is disturbed. In this case waves move outwards across the water surface from the point of disturbance. Wave motion along the string. If the end of a string is rapidly displaced and returned to its original position, the disturbance travels along the string, away from the source, as a single wave, which we call a wave pulse. Wave motion is generating, when disturbance is generating in a wave source and the disturbance is propagating in time and in space.

3 Special waves: Mechanical waves: when the disturbance generates in elastical mediums and propagates in the space. Electromagnetic waves: when electromagnetic oscillations generated in resonant circuit radiate into the space using open resonant circuit (antenna). This way the electromagnetic waves propagates in the space. Shock waves: When the time duration of the disturbance is very short (instantaneous). Traveling waves: When the wave source produces waves continuously. Periodic waves: In the case, when the disturbance is a periodic function of the time, the waves called periodic waves. Harmonic waves: When the disturbance is sinusoidal function of the time such a waves called harmonic waves. We shall discuss harmonic waves. Comment: Propagation of mechanical waves needs elastic medium, but electromagnetic waves can propagate in vacuum (without any elastic mediums), too. Therefore, electromagnetic waves are different type of waves then mechanical waves. For example: sound is mechanical wave, and light and radio waves are electromagnetic waves.

4 Definitions, elements: Definition (Field of the wave): part of the space where the disturbance propagates. Definition (Wavelength): the wavelength of a sinusoidal wave is the spatial period of the wave the distance over which the wave's shape repeats. It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. Wavelength is commonly designated by the Greek letter lambda (λ). The concept can also be applied to periodic waves of non-sinusoidal shape. The term wavelength is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids. The SI unit of wavelength is the meter.

5 Definitions, elements: Definition (Phase velocity): Speed of the traveling or propagating disturbance is v. The v is called phase velocity (speed of propagation). Definition (Period of the wave or period of time): It is the time during the wave propagates to distance from a well-defined point. T = λ v Definition (Frequency): Reciprocal value of the T period of time. Frequency is commonly designated by the letter f. f = 1 T = v λ Definition (Amplitude of the wave): The amplitude is defined as the maximum disturbance of the medium from equilibrium, commonly indicated by A.

6 Main categories of waves: Longitudinal wave: In a longitudinal wave the disturbance from equilibrium is parallel to the direction of propagation of the waves, or the direction of their velocity v. Most important example for the longitudinal wave is the sound wave. Sound waves are compression waves in air illustrated here:

7 Main categories of waves: Transverse wave: In a transverse wave the disturbance from equilibrium (axis of y, equilibrium: y=0), is perpendicular to the direction in which the wave is propagating, i.e., it is perpendicular to the direction of the wave velocity v. Most important examples for the transverse waves are: waves across the water surface, or waves along the string.

8 Another main types of waves: Traveling waves along a line: waves move along a string. Three-dimensional wave: When the disturbance propagates into all three-dimension of the space. For example: Light waves. Surface of the wave: All points, where the wave has same phase (state of the disturbance). Plane wave: The surface of the wave can be represented by a plane. Spherical waves and wave normal: The surfaces of the waves are spheres. Line perpendicular to the wave surfaces is the wave normal.

9 Wave function The physical quantity characterizes the disturbance states of a wave is called wave function. It is commonly indicated by ψ. Wave function can depend on the space coordinate and the time of a wave space, in other words, in general ψ = ψ( r, t). Some examples for the wave functions are: move of the disturbance, pressure-modification in a medium at a well-defined point, or electric or magnetic field. Main condition of generation of a harmonic wave is: the disturbance is harmonic function of the time. In other words: ψ = ψ 0 sin(ωt + α)

10 Energy and intensity of a wave: Energy of the wave: One of the most important property of a wave motion is that energy propagates in a wave. The wave source gives its energy to the space, and the space transmits the energy from a point to another point. This way, the wave field can be specified by the energy density. Energy density: Energy density is the ratio of the energy value and the volume holds the energy. Energy density is commonly signed by w and its dimension is J/m 3. w = E V or w = de dv Intensity of the wave, or wave intensity: It is the energy quantity propagates through a normal surface during the time element. Normal surface element means element which is perpendicular to the direction of propagation. I = dp da = dw da dt = w da ds da dt = w v

11 Properties of waves: Properties of waves reflection, refraction, interference, diffraction, polarization will be discussed in detail at section of Optics.