What Is a Mechanical Wave?

The propagation of mechanical vibration in a medium is called a mechanical wave. There are similarities and differences between mechanical waves and electromagnetic waves. Mechanical waves are generated by mechanical vibrations, and electromagnetic waves are generated by electromagnetic oscillations. The propagation of mechanical waves requires a specific medium, and the propagation speed is different in different media. It cannot be transmitted in a vacuum at all. Electromagnetic waves (such as light waves) can propagate in a vacuum; mechanical waves can be shear waves and longitudinal waves, but electromagnetic waves can only be shear waves; many physical properties of mechanical waves and electromagnetic waves, such as refraction and reflection, are consistent, and the physical quantities describing them are identical. Common mechanical waves are: water waves, acoustic waves, and seismic waves.

Chinese name: Mechanical wave
Foreign name: mechanical wave

Forming conditions: Wave source
Classification: S-wave and P-wave

Mechanical wave formation propagation

Introduction

The relationship between mechanical waves and mechanical vibrations ^[1]

Mechanical vibration generates mechanical waves. There must be a medium for the transmission of mechanical waves. Mechanical vibrations do not necessarily produce mechanical waves.

Forming conditions

Wave source

A wave source is also called a vibration source, which refers to an object that can maintain the propagation of vibration, continuously input energy, and can emit waves or the initial position of the object. The wave source is a necessary condition for the formation of mechanical waves and a necessary condition for the formation of electromagnetic waves.

The wave source can be considered to be the first particle that starts to vibrate. After the wave source starts to vibrate, other particles in the medium will be forced to vibrate at the frequency of the wave source. The frequency of the wave source is equal to the frequency of the wave.

medium

A medium in the broadest sense can be another substance containing one substance. In mechanical waves, a medium refers to a substance through which mechanical waves propagate. When there is only a wave source and no medium, mechanical waves are not generated, for example, an alarm clock in a vacuum cannot make a sound. The propagation rate of mechanical waves in a medium is determined by the inherent properties of the medium itself. In different media, the wave speed is different.

The table below shows the propagation speed of sound waves in different media at 0 ° C. The data is taken from "Standard High School Curriculum Standard Experiment Textbook-Physics (Elective 3-4)" (2005) ^[2] . Unit v / m · s ^ -1

medium	air	Pure water	brine	rubber	cork	copper	iron
Wave speed	332	1490	1531	30 50	480	3800	4900

Propagation mode

Particle motion

During the propagation of a mechanical wave, each particle only performs simple up-and-down (left and right) harmonic resonance, that is, the particle itself does not advance with the propagation of the mechanical wave, that is, a particle motion of the mechanical wave is performed along a horizontal straight line . For example, human vocal cords do not leave the mouth with sound waves. Simple harmonic motion is a constant amplitude vibration, which can be considered as a motion of energy conservation in the ideal state. Damped vibration is a motion in which energy is gradually lost.

In order to explain the characteristics of the particle motion during the propagation of mechanical waves, rope waves (bottom right) have been introduced as an example. Other forms of mechanical waves are the same ^[2] .

Rope wave The rope wave is a simple transverse wave. In daily life, we pick up one end of a rope and shake it once, and we can see a waveform propagating on the rope. If the wave is shaken up and down continuously, a rope is formed. Wave ^[2] .

The rope is divided into many small parts, and each small part is regarded as a mass point. There is an elastic interaction between two adjacent mass points. After the first particle vibrates under external force, it will drive the second particle to vibrate, but the vibration of the second particle is behind the former. In this way, the vibration of the previous particle drives the vibration of the next particle, which in turn drives the vibration, and the vibration occurs in the area that propagates to the distance, thereby forming a rope wave. If we pick any point on the rope and tie the red cloth strip, we can also find that the red cloth strip only vibrates up and down and does not follow the wave ^[2] .

From this, we can find that each particle in the medium only conducts simple harmonic vibration (which can be up and down, or left and right) when the wave propagates. Mechanical waves can be regarded as a form of motion. The particle itself Does not move in the direction of wave propagation.

There are many ways to determine the direction of particle movement, such as comparing the movement of the previous particle; you can also use "uphill down, downhill" to determine, that is, along the wave's propagation direction, the particles moving away from the equilibrium position move downward. , Move the particle point away from the equilibrium position upward.

Communication essence

In the process of mechanical wave propagation, the relatively static particles in the medium will vibrate with the propagation of the mechanical wave, which indicates that these particles have obtained energy, which is sequentially transmitted from the wave source through the previous particles. Therefore, the essence of mechanical wave propagation is the propagation of energy. This energy can be small or large. The tidal energy of the ocean can even be used to generate electricity. This is to maintain the energy transmitted by mechanical waves (water waves) into electrical energy.

Huygens principle

Huygens' principle is used to explain the propagation of spherical and plane waves, and it can also explain the phenomenon of wave reflection and diffraction.

Based on the summary of many experiments, the Dutch scientist Huygens proposed that each point (there are countless) on the wave front in the medium can be regarded as a new wave source, and these new wave sources emit wavelets. After a certain period of time, the envelope surfaces of these wavelets constitute the wave surface at the next moment ^[2] .

According to Huygens' principle, we can explain how the wave surface of a spherical wave is formed. In the figure on the right, the wave surface of the wave at point t at time t is a spherical surface S1. Each point on the spherical surface can be regarded as a new one. Point wave sources, they each emit spherical wavelets forward, and the next time (t + t) a new wave surface S2 is the tangent envelope surface of these wavelet waves; the same is true for plane waves.

Limitations of Huygens' Principle

did not explain the intensity distribution of the wavelet;

It does not explain why the wave can only propagate forward, but not backward.

Later, Fresnel made important supplements to Huygens' principle, forming Huygens-Fresnel's principle, these defects were overcome.

Mechanical wave classification

Overview of mechanical waves

As the mechanical wave propagates, the particles in the medium vibrate. According to the relationship between the vibration direction of the particle and the propagation direction of wave propagation, mechanical waves can be divided into two types: transverse waves and longitudinal waves.

Mechanical wave shear wave

In physics, a wave whose particle's vibration direction is perpendicular to the wave's propagation direction is called a transverse wave. In the transverse wave, the highest point of the convexity is called the crest, and the lowest point of the concave is called the trough.

Rope waves are common shear waves ^[2] .

Mechanical wave P-wave

In physics, waves whose particle's vibration direction is in the same straight line as the wave's propagation direction are called longitudinal waves. Particles vibrate back and forth as the longitudinal wave propagates. The densest part is called the dense part, and the sparsest part is called the sparse part.

Sound waves are common longitudinal waves ^[2] .

Mechanical wave description

Wave curve

If you take a picture at a certain moment of the rope fluctuation, you can get the waveform at that moment. This waveform is composed of particles on the rope with different displacements at the same time. If you add a coordinate system to the waveform, you can get an image of the wave at that moment. The abscissa x represents the equilibrium position of each particle along the wave propagation direction, and the ordinate y represents the size of each particle leaving the equilibrium position. The prescribed displacement direction is positive. On the coordinate plane, the corresponding points are described by the x and y values of each particle at a certain time, and connected with a smooth curve to obtain the image of the wave at that time, also known as the waveform curve or waveform. On the wave image, the direction of wave propagation is usually indicated by arrows.

The waveform curve is different from the vibration image. The vibration image is the displacement of a vibrating object at different times, and the waveform curve is the displacement of all particles at a specific moment.

On the waveform curve, we can read out the displacement and direction of all particles at the same time, as well as physical quantities such as wavelength and period.

Simple harmonic wave

If each particle in the medium makes a simple harmonic motion, the wave it forms is the most basic and simple wave, called a simple harmonic, and its waveform is a sine (or cosine) curve. Other waves can be regarded as a combination of several simple harmonics ^[2] .

Physical description

The physical quantities that describe mechanical waves are also applicable to electromagnetic waves. Therefore, "mechanical waves" are referred to as "waves" for short.

Wavelength

Along the wave's propagation direction, the distance between two adjacent particles whose displacements and vibration directions are always the same in the relative equilibrium position is called the wavelength, and is often used ^[2] . In transverse waves, the wavelength is equal to the length of "peak-to-peak" or "valley-to-trough"; in longitudinal waves, the wavelength is equal to the length of "dense-dense" or "sparse-dried".

Frequency and period

The time it takes for any particle on the wave to complete a full vibration is called the period, which is often expressed by T , and the unit is s ; the number of times that a particle in the medium completes full vibration in a unit of time is called the frequency of the wave, and f is often used, and the unit is Hz . Frequency is the inverse of the period.

Wave speed

Wave velocity is the distance that a wave travels through a medium per unit of time. It is the product of wavelength and frequency (v = f) and represents the wave's propagation speed. The propagation speed of mechanical waves in a specific medium is fixed ^[2] .

Mechanical wave physical properties

The physical properties of mechanical waves are also applicable to electromagnetic waves. Therefore, "mechanical waves" are simply referred to as "waves"

Refraction of mechanical waves

In physics, we refer to the phenomenon in which the propagation direction of a wave changes from one medium to another in the process of propagation.

In the refraction of a wave, the angle between the wave line and the normal of the incident wave is called the incident angle and is represented by i ; the angle between the wave line and the normal of the refracted wave is called the refraction angle and is represented by r .

Law of refraction

Further research shows that when the wave is refracted, the angle of incidence and the angle of refraction have the following relationship

(sini) / (sinr) = v1 / v2 = 1 / 2

v is the wave speed; is the wavelength

This law is called Snell's law in optics.

Reflection of mechanical waves

In physics, the phenomenon that waves reflect back when they encounter obstacles and continue to propagate is called wave reflection

Law of reflection

The reflected wave line, the incident wave line and the normal line are in the same plane, the reflected wave line and the incident wave line are respectively located on both sides of the normal line, and the incident angle is equal to the reflection angle.

Interference of mechanical waves

Interference of waves The superposition of two waves of the same frequency strengthens the vibration in some areas, weakens the vibration in some areas, and separates the areas where the vibration is strengthened and the areas where the vibration is weakened. This phenomenon is called wave interference.

A necessary condition for interference is that the frequency of the two waves must be the same or have a fixed phase difference. If the frequencies of the two waves are different or the two wave sources do not have a fixed phase difference (phase difference), the amplitude of each particle on the wave changes with time when superimposed on each other, there is no region where the vibration is always strengthened or weakened, so it cannot produce stability Interference pattern cannot form interference pattern.

The coherence conditions for the two columns of waves are:

Same frequency

The vibration direction is the same

Same phase or constant phase difference

Wave superposition principle

The principle of wave superposition includes two points:

The waves excited by each wave source can propagate independently in the same medium. After they meet, they are separated, and their propagation conditions (frequency, wavelength, propagation direction, cycle are equal) are the same as when they are not encountered, and they do not interfere with each other, just like other waves Does not exist

The vibration of each point in the meeting area is the vector sum of the vibration caused by each wave at that point.

Diffraction of mechanical waves

Diffraction of waves Diffraction is a unique phenomenon of waves. All waves can be diffracted.

Waves can propagate around obstacles. This phenomenon is called wave diffraction.

Obvious diffraction conditions are observed: Only when the width of the slits or holes or the size of the obstacle is similar to or smaller than the wavelength, can the obvious diffraction phenomenon be observed.

Relative to the wavelength, the larger the linearity of the obstacle, the less obvious the diffraction phenomenon, and the smaller the linearity of the obstacle, the more obvious the diffraction phenomenon.

Mechanical Doppler

Standing wave

A wave formed by superimposing two columns of waves with the same frequency and amplitude, the same vibration direction, and the opposite propagation direction. When the wave propagates in the medium, its waveform keeps advancing, so it is called traveling wave; after the above two columns of waves are superimposed, the waveform does not advance, so it is called standing wave.

The wavelength can be determined by measuring the distance between two adjacent nodes. Various musical instruments, including stringed, wind and percussion instruments, produce sounds due to standing waves. To obtain the strongest standing wave, the length L of the air column in the string or tube must be equal to an integer multiple of half the wavelength, that is, k is an integer and is the wavelength. Therefore, the standing wave wavelength that can exist in a string or tube is, the corresponding vibration frequency is, and is the wave speed. When k = 1, it is called the fundamental frequency. In addition to the fundamental frequency, there may be a multiple of frequency kn1.

The wave formed by the incident wave (propulsion wave) and the reflected wave interfering with each other no longer propels (only the antinodes vibrate up and down, and the nodes do not move) are called standing waves. Standing waves often occur in front of steep coastal walls or upright hydraulic structures. Although the sea surface near the steep wall periodically rises and falls over time, the sea water flows back and forth, but it does not propagate forward. The water surface is basically horizontal. This is because the incident wave and reflected wave interfere with each other due to the limitation of the shore wall. Forming. The wave surface rises and falls periodically with time, and every half a wavelength has a section with the largest wave surface rise and fall, called an antinode; when the wave surface rise and fall amplitude is 0, it is called a node. The horizontal distance between two adjacent nodes is still half a wavelength, so the wavefront of the standing wave contains a series of antinodes and nodes. Although the abdominal nodes are in phase, the wavefronts at the antinodes have periodic changes, but this section The horizontal position is fixed and the position of the nodes is also fixed. This is exactly the opposite of the phenomenon in which the crests and troughs of the progressing wave move in the horizontal direction. The shape of the standing wave does not propagate, hence the name standing wave. When the wave surface is at the highest and lowest positions, the horizontal velocity of the particle is zero, and the wave surface's lifting speed is also zero. When the wave surface is at the horizontal position, the absolute value of the flow velocity is the largest, and the wave surface is also the fastest. Some characteristics.