Linear waves are described by linear equations, i.e. those where in each term of the equation the dependent variable and its derivatives are at most first degree (raised to the first power). This means that the superposition principle applies, and linear combinations of simple solutions can be used to form more complex solutions.
What is linear wave theory?
The most elementary wave theory, referred to as small-amplitude or linear wave theory, was developed by Airy (1845). This nomenclature derives from the simplifying assumptions of its derivation. Additionally, it represents a first approximation resulting from a formal perturbation procedure for waves of finite amplitude.
What is a line wave?
Waves in general
- Wave equation, general
- One-way wave equation, for waves running in pre-defined direction
- Wave propagation, any of the ways in which waves travel
- Interference (wave propagation), a phenomenon in which two waves superpose to form a resultant wave
- Mechanical wave, in media transmission
- Wave Motion (journal), a scientific journal
What is the formula for speed of a wave?
Just use our wavelength calculator in the following way:
- Determine the frequency of the wave. For example, f = 10 MHz.
- Choose the velocity of the wave.
- Substitute these values into the wavelength equation λ = v/f.
- Calculate the result.
- You can also use this tool as a frequency calculator.
How can a sine wave represent a longitudinal wave?
Sine wave - transverse representation of a longitudinal wave. Uniform Circular Motion Movement around a circle can be translated into displacement over time - looks just like a sine wave!
What is linear and nonlinear wave shaping?
Either the shape of the wave is attenuated or the dc level of the wave is altered in the Non-linear wave shaping. The process of producing non-sinusoidal output wave forms from sinusoidal input, using non-linear elements is called as nonlinear wave shaping.
What is linear wave equation?
Taking the ratio and using the equation v = ωk yields the linear wave equation (also known simply as the wave equation or the equation of a vibrating string), ∂2y(x,t)∂t2∂2y(x,t)∂x2=−Aω2sin(kx−ωt+ϕ)−Ak2sin(kx−ωt+ϕ)=ω2k2=v2, ∂2y(x,t)∂x2=1v2∂2y(x,t)∂t2. Equation 16.3.
What are the types of wave shaping circuits?
The common periodic waveforms include the square wave, the sine and rectified sine waves, the sawtooth and triangular waves, and the periodic arbitrary wave. The arbitrary wave can be made to conform to any shape during the duration of one period.
Are sound waves linear?
Most sound waves behave as linear waves since they produce pressure fluctuations in air that are very small compared to the atmospheric pressure.
What is frequency of a wave?
In physics, the term frequency refers to the number of waves that pass a fixed point in unit time. It also describes the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.
What is linear network?
In summary, a linear network is a network that exhibits constant parameters, i.e., resistance and inductance. In other words, these parameters do not change with the changes in voltage or current. Working through a linear network is simpler than one might think due to its consistency of characteristics.
What are non linear elements?
Nonlinear elements – these are elements in which the relation between voltage and current is a nonlinear function. An example is a diode, in which the current is an exponential function of the voltage.
What is clipper and clamper circuit?
A clipper circuit clips or removes a portion of an AC signal. A clamper circuit shifts the DC level of the waveform. A clipper circuit is also known as a voltage limiter, slicer, etc. A clamper is also known as a voltage multiplier or DC level shifter. It is made of diode and resistor.
Which calculus allows the linear wave equation to be gotten from a Lagrangian density?
In the case of the Dirac equation, the variational calculus allows the linear wave equation (1) to be gotten from a Lagrangian density:
What is superposition in waves?
This is called the principle of superposition. The displacement due to two waves is generally the algebraic sum of the displacements due to the two waves separately. Waves that obey the superposition principle are called linear waves and waves that do not are called nonlinear waves. It is found experimentally that most of the waves encountered in nature obey the superposition principle. Shock waves produced by an explosion or a jet moving at supersonic speeds are uncommon examples of waves that do not obey the superposition principle. In this text, only linear waves will be considered. Two harmonic waves reinforce each other or cancel depending upon whether or not they are in phase (in step) with each other. This phenomenon of reinforcement or cancellation is called interference.
How are western boundary currents modeled?
Western boundary currents have been modeled in a rotating cylinder of fluid in which the base is a sloping plane that creates variable depth. It is readily shown that, in an unstratified fluid, the variable depth has the same effect on the flow as the latitudinal variation of the Coriolis parameter has on the atmosphere and the ocean. Experiments and theory confirm that this is the crucial ingredient in the formation of western boundary currents.
Is ultrasonic wave propagation linear?
All the theory concerning tissue ultrasonic properties and beam focusing previously presented was under the assumption of finite-amplitude, linear wave propagation. Actually, it is well known that high-amplitude transmitted medical ultrasonic waves undergo nonlinear transmission in tissue (Muir, 1980 ). Nonlinear ultrasonic waves have amplitude-dependent acoustic velocities ( Beyer, 1969 ). This causes waveform distortion, shock wave formation, and harmonic generation ( Muir and Carstensen, 1980 ). The nonlinear parameters of tissue have been studied for some time ( Law et al., 1985 ).
Is functional L invariant?
The functional L is invariant under the Poincaré group, generated by time and space translations and the Lorentz transformations λ > 1, c ≠ 0:
Is harmonically distorted ultrasonic transmit beam narrower?
It has been demonstrated recently that harmonically distorted ultrasonic transmit beam patterns are narrower and have lower side-lobe levels and shorter pulse lengths than undistorted fundamental frequency beams ( Ward et al., 1997 ). So if nonlinear shock wave formation can be demonstrated not to cause any bioeffects in tissue ( NCRP, 1983 ), the high-pressure amplitudes used in ultrasonic imaging equipment will produce only benefits for the patient.
What is the wave in math?
A wave is a time evolution phenomenon that we generally model mathematically using partial differential equations (PDEs) which have a dependent variable u (x,t) (representing the wave value), an independent variable time t and one or more independent spatial variables xinmathbb {R}^ {n} , where n is generally equal to 1,2 ;textrm {or}; 3 . The actual form that the wave takes is strongly dependent upon the system initial conditions, the boundary conditions on the solution domain and any system disturbances .
How to solve linear and nonlinear evolutionary wave problems?
Linear and nonlinear evolutionary wave problems can very often be solved by application of general numerical techniques such as: finite difference, finite volume, finite element, spectral, least squares, weighted residual (e.g. collocation and Galerkin) methods, etc. These methods, which can all handle various boundary conditions , stiff problems and may involve explicit or implicit calculations, are well documented in the literature and will not be discussed further here. For general texts refer to [Bur-93], [Sch-94], [Sch-09] , and for more detailed discussion refer to [Lev-02], [Mor-94], [Zie-77] .
What is chemical wave?
Chemical waves - concentration variations of chemical species propagating in a system [Ros-88].
What are waves in science?
Waves occur in most scientific and engineering disciplines, for example: fluid mechanics, optics, electromagnetism, solid mechanics, structural mechanics, quantum mechanics, etc. The waves for all these applications are described by solutions to either linear or nonlinear PDEs.
Why do waves not travel in a straight line?
Wave crests do not necessarily travel in a straight line as they proceed - this may be caused by refraction or diffraction.
Which wave is polarized in the direction of the wave propagation?
They include: seismic S (secondary) waves, and electromagnetic waves, E (electric field) and H (magnetic field), both of which oscillate perpendicularly to each other as well to the direction of propagation of energy. Light , an electromagnetic wave, can be polarized (oriented in a specific direction) by use of a polarizing filter .
Which type of wave is irrotational?
Irrotational waves are of the longitudinal type, or P-waves. For solenoidal waves, which can vibrate independently in the y and z directions but not in the direction of propagation x , we have nablacdotvarrho=0 and equation ( 18) reduces to the linear wave equation.
How to do linear wave shaping?
Linear Wave Shaping & Different Types of Waveforms 1 To hold the waveform to a particular d.c. level. 2 To generate one wave form the other 3 To limit the voltage level of the waveform of some presenting value and suppressing all other voltage levels in excess of the present level. 4 To cut-off the positive and negative portions of the input waveform.
What is a waveform that increases linearly with time?
4 (b) is called sawtooth waveform. It is also called sweep waveform or time-base waveform. The sawtooth waveform is used in the scanning circuit of cathode ray oscilloscopes and televisions.
What is a triangular wave?
A waveform which increase linearly with time to a voltage level V for a time T/2 and then decreases linearly to its original level for a time T/2 and is repetitive with a period T as shown in Fig. 4 (a) is called triangular waveform. It may be noted from this figure, that a triangular wave may be considered as the sum of ramp voltage, which incre.ases at a rate of 2V/T for a time T/2 and the ramp voltage which decreases at a rate of —2V/T for the remaining time T/2. The triangular waveform is used in scanning circuits, where a uniform left-to-right scan is required as in computer displays. These are also used in timing circuit for electronics applications.
What is a non sinusoidal wave?
Non-sinusoidal Waveforms. Any waveform whose shape is different from that of sinusoidal wave is called a non -sinusoidal waveform. For example pulse square, symmetrical square triangular and saw-tooth are non-sinusoidal waves. When one quantity is dependent upon some other variable quantity varies with respect to others.
What is a waveform that maintains itself at one constant voltage level?
2 (a) is called a square waveform. The square waveform is used in digital electronic circuits, radars and as synchronizing pulses in television.
What is wave shaping?
The wave shaping is used to perform any one of the following functions. To hold the waveform to a particular d.c. level. To generate one wave form the other. To limit the voltage level of the waveform of some presenting value and suppressing all other voltage levels in excess of the present level.
What is a square waveform?
A square waveform for which T 1 = T 2 = T/2 as shown in Fig. 3 (b) is called a square waveform. It may be noted that because of the symmetry, the voltage levels V 1 and V 2 are equal and opposite V 1 = —V 2. The symmetrical square waveform is very useful in digital electronic circuits.
What is a wave in a circuit?
Electronic Circuits - Linear Wave Shapping. A Signal can also be called as a Wave. Every wave has a certain shape when it is represented in a graph. This shape can be of different types such as sinusoidal, square, triangular, etc. which vary with respect to time period or they may have some random shapes disregard of the time period.
What are the elements used to shape a signal?
Linear elements such as resistors, capacitors and inductors are employed to shape a signal in this linear wave shaping. A Sine wave input has a sine wave output and hence the nonsinusoidal inputs are more prominently used to understand the linear wave shaping.
What is the simplest wave?
Mathematically, the simplest wave is a sinusoidal plane wave in which at any point the field experiences simple harmonic motion at one frequency.
How do waves work?
However materials may be characterized as "lossy" if they remove energy from a wave, usually converting it into heat. This is termed "absorption." A material which absorbs a wave's energy, either in transmission or reflection, is characterized by a refractive index which is complex. The amount of absorption will generally depend on the frequency (wavelength) of the wave, which, for instance, explains why objects may appear colored.
How do mechanical waves propagate?
A mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves are variations of the local pressure and particle motion that propagate through the medium.
What type of wave has nulls?
In a standing wave , the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero. The types of waves most commonly studied in classical physics are mechanical and electromagnetic. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibrium.
What are some examples of mechanical waves?
Other examples of mechanical waves are seismic waves, gravity waves, surface waves, string vibrations (standing waves), and vortices. In an electromagnetic wave (such as light), coupling between the electric and magnetic fields which sustains propagation of a wave involving these fields according to Maxwell's equations.
How many positions are there in the bottom of the wave?
Identical waves from two sources undergoing interference. Observed at the bottom one sees 5 positions where the waves add in phase, but in between which they are out of phase and cancel.
What is a standing wave in a recorder?
For example, the sound pressure inside a recorder that is playing a "pure" note is typically a standing wave, that can be written as
What is a plane wave?
In physics, a plane wave is a special case of wave or field: a physical quantity whose value, at any moment, is constant over any plane that is perpendicular to a fixed direction in space.
What is standing wave?
A standing wave is a field whose value can be expressed as the product of two functions, one depending only on position, the other only on time. A plane standing wave, in particular, can be expressed as
What is a monochromatic plane wave?
The term is also used, even more specifically, to mean a "monochromatic" or sinusoidal plane wave: a travelling plane wave whose profile#N#G ( u ) {displaystyle G (u)}#N#is a sinusoidal function. That is,
Why can't plane waves exist?
φ {displaystyle varphi }. is its "phase". A true plane wave cannot physically exist, because it would have to fill all space. Nevertheless, the plane wave model is important and widely used in physics.
What Is Longitudinal Wave?
Longitudinal waves are the waves where the displacement of the medium is in the same direction as the direction of the travel of the wave.
What is compression in a longitudinal wave?
A compression in a longitudinal wave is a region where the particles are the closest together while rarefaction in a longitudinal wave is a region where the particles are spread out.
What is the condition for sound waves to travel through gas?
For a sound wave to travel through the gas, the required condition is an adiabatic condition. This is because when the sound waves travel they produce compressions and rarefactions which results in the generation of heat. Therefore, for the waves to travel through the gas, the temperature must be constant.
When does rarefaction occur in a longitudinal wave?
Rarefaction in a longitudinal wave takes place when the particles are farthest apart from each other.
What is an example of a sound wave?
An example of sound waves in a longitudinal direction is the tuning fork. In Sound waves, the amplitude of the wave is the difference between the maximum pressure caused by the wave and the pressure of the undisturbed air. The propagation speed of sound depends upon the type, composition of the medium, and temperature through which it propagates.
What is mechanical wave?
In Physics, we define wave as an oscillation about a fixed point, that is accompanied by the transfer of energy. When the transfer of energy takes place through a medium due to oscillation, the resultant wave is termed as a mechanical wave.
What is pressure wave?
The pressure wave is defined as the propagation of disturbance in a medium as the pressure varies.
