How Do Elastic Waves Propagate Through Different Materials?
Before studying elastic waves, we should know the definition of a wave. A wave can be defined as the disturbance produced in a medium that carries energy without a net movement of particles. It may take the form of elastic deformation, pressure changes, electric or magnetic strength changes, electric potential changes, and temperature changes. A wave is an oscillating flow or movement of energy through a medium such as space or mass. In this article, we understand the elastic medium and what is a medium in physics and the factors affecting wave propagation.
Definition of Elastic Waves
In a solid, liquid, or gaseous medium, an elastic disturbance propagates. Waves formed in the earth's crust during earthquakes, as well as sound waves and ultrasonic waves in liquids and gases, are examples of elastic waves. When elastic waves propagate, the energy associated with elastic deformation gets transferred in the absence of a flow of matter, which occurs only in special cases, like during an acoustic wind. Every harmonic elastic wave is characterized by the vibration frequency and amplitude of the particles of the medium, phase and group velocities, a wavelength, and the distribution of displacements and stresses over the wavefront. The special features of elastic waves are their phase and group velocities. It is independent of the wave amplitude and the wave geometry. An elastic wave can be either a plain, spherical, or cylindrical wave.
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The above diagram represents an elastic wave.
The elastic waves are based on the principle of restoring force acting on the particles in matter. When a particle is moved from its original position (for example by an excitation), a restoring force starts acting on it. This force can be calculated by Hooke’s law and acts in the direction of the original direction. As the particles in the matter are linked to each other the displacement of one particle leads to a displacement of its surrounding particles. This leads to the propagation of energy through the medium.
Elastic waves can be divided into transversal and longitudinal waves. The waves having oscillations perpendicular to the direction of propagation are called transverse waves. And, the waves having oscillations parallel to the direction of propagation are known as longitudinal waves. Both types of elastic waves need a medium to propagate.
Diagram of transverse and longitudinal waves are shown below:
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An elastic wave is produced due to a disturbance produced at a point in a medium.
The disturbed particle interacts with a particle in its neighbour and its energy gets handed over to the next particle (due to the inertia of the medium).
The disturbed particles come back to the equilibrium position (due to the elasticity of the medium).
What is a Medium in Physics?
In physics, the medium is defined as the substance that transfers the energy, or light from one substance to another substance or from one place to another or from one surface to another. The medium acts as a carrier here. The medium can transfer any form of energy such as sound waves, light, and heat.
The substance through which a wave can propagate is referred to as medium. Water is the medium of ocean waves. Air is the medium of sound waves. The electric, as well as magnetic fields, are the medium of light. People are the medium of a stadium wave. The Earth is the medium of seismic waves (such as earthquake waves). Cell membranes are the medium of nerve impulses. Transmission lines are the medium of alternating current and electric power.
Elastic Medium
The medium can change its shape when any deforming force is applied and later it comes back to its original shape when the deforming force is removed are known as elastic medium. The examples are- air, water.
Elastic Wave Propagation
An elastic wave generally travels through a material or fluid, or on its surface, without causing any permanent structural or physical changes. Waves that propagate through water, sound moving through the air, as well as energy moving through solid materials such as the Earth are often described as elastic waves. Propagation can also be analyzed mathematically, as the height, length, and timing of an elastic wave can be visualized with the help of graphs. Special ultrasonic cameras can be used to image the movement across a solid surface such as a sheet of metal or paper.
The properties of elastic waves are influenced by the elastic properties of the propagation medium. This consists of the number of different modes which can propagate and their velocities.
Elastic Waves in Solids
The effect of a sharply applied, localized disturbance produced in a medium soon will transmit or spread to other parts of the medium. This phenomenon is familiar to everyone in various situations such as the transmission of sound in the air, the spreading of ripples on a pond of water, and the transmission of seismic tremors in the earth or in the transmission of radio waves. The propagation of disturbances in various media like gas, liquid as well as solid has many features which are common. The physical basis for the propagation of a disturbance is mainly based on the interaction of the discrete atoms of the medium. In solid as we will as in fluid mechanics, the medium is regarded as continuous, therefore the properties such as density or elastic constants are considered to be continuous functions that represent averages of microscopic quantities.
FAQs on Understanding Elastic Waves in Physics
1. What are elastic waves in Physics?
Elastic waves are a type of mechanical wave that transfers energy through a medium by causing its particles to oscillate. The wave propagates due to the medium's elastic properties, which allow it to return to its original shape after being deformed. Essentially, they are disturbances that travel through solids, liquids, or gases without any net transfer of mass.
2. What are the essential properties a medium must have for elastic waves to travel through it?
For an elastic wave to propagate, a medium must possess the following key properties:
- Elasticity: This property allows the particles of the medium to store potential energy and return to their original position after being displaced.
- Inertia: This property, related to the medium's density, allows the particles to store kinetic energy and overshoot their equilibrium position, thus passing the disturbance to the next particles.
- Minimum Friction: There should be minimal internal friction between the particles so that the wave's energy does not dissipate quickly and can travel over longer distances.
3. Can you provide some real-world examples of elastic waves?
Elastic waves are very common in our daily lives and in nature. Some key examples include:
- Sound Waves: The propagation of sound through air, water, or a solid is a primary example of an elastic wave.
- Seismic Waves: During an earthquake, the Earth's crust transmits energy through P-waves (longitudinal) and S-waves (transverse), both of which are elastic waves.
- Waves on a String: When a guitar string is plucked, a transverse elastic wave travels along its length.
- Ultrasonic Waves: These are high-frequency elastic waves used in medical imaging (ultrasound) and SONAR systems.
4. Can elastic waves be both transverse and longitudinal?
Yes, elastic waves can be classified as either transverse or longitudinal, depending on the direction of particle movement relative to the wave's propagation.
- In longitudinal waves, the particles of the medium oscillate parallel to the direction of energy transfer. Sound waves are a classic example.
- In transverse waves, the particles oscillate perpendicular to the direction of energy transfer. Waves on a taut string are a common example.
The type of wave a medium can support depends on its physical properties, particularly its ability to resist shear forces.
5. Why can transverse elastic waves travel through solids but not through fluids like liquids and gases?
This difference is due to the fundamental properties of solids and fluids. Transverse waves propagate by exerting a shear force on the medium, meaning one layer of the medium pulls the next layer sideways. Solids have a definite shape and strong intermolecular forces, giving them a shear modulus that allows them to resist this force and propagate the wave. In contrast, fluids (liquids and gases) cannot sustain a shear force; they simply flow. As they lack rigidity, they cannot propagate transverse waves.
6. How are sound waves a specific example of elastic waves?
Sound waves are fundamentally a type of longitudinal elastic wave. Their propagation is entirely dependent on the elastic properties of the medium they travel through. A sound wave moves by creating a series of compressions and rarefactions. For the medium to compress and then expand back, it must be elastic. The speed at which sound travels is determined by the medium's elasticity (e.g., Bulk Modulus) and its inertia (density). Without an elastic medium, sound cannot be transmitted.
7. What is the fundamental difference between elastic waves and electromagnetic waves?
The primary difference lies in their nature and requirement for a medium.
- Medium Requirement: Elastic waves are mechanical waves and absolutely require a material medium (solid, liquid, or gas) to travel. Electromagnetic (EM) waves, such as light or radio waves, do not require a medium and can travel through the vacuum of space.
- Nature of Wave: Elastic waves are the vibrations of particles in a medium. EM waves are oscillations of mutually perpendicular electric and magnetic fields.
- Speed: The speed of elastic waves is determined by the medium's properties (e.g., density and elasticity), whereas the speed of EM waves in a vacuum is a universal constant, c (approximately 3 x 10⁸ m/s).
8. What determines the speed of an elastic wave in a medium?
The speed of an elastic wave is an intrinsic property of the medium itself, not the wave's source. It generally depends on the ratio of the medium's elastic property to its inertial property. For instance:
- In a solid rod, speed depends on its Young's Modulus (Y) and density (ρ).
- In a fluid, speed depends on its Bulk Modulus (B) and density (ρ).
- On a stretched string, speed depends on the tension (T) and its linear mass density (μ).
