Bjerknes Force
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Bjerknes Force
Bjerknes forces are translational forces on bubbles in a sound wave. The phenomenon is a type of acoustic radiation force. ''Primary'' Bjerknes forces are caused by an external sound field; ''secondary'' Bjerknes forces are between pairs of bubbles in the same sound field. They were first described by Vilhelm Bjerknes in his 1906 ''Fields of Force''. Theory The force on a small particle in a sound wave is given by: : F = - V \nabla P where V is the volume of the particle, and \nablaP is the acoustic pressure gradient on the bubble. Assuming a sinusoidal travelling wave, the time-averaged pressure gradient over a single acoustic cycle is zero, meaning a solid particle (with fixed volume) experiences no net force. However, because a bubble is compressible, the oscillating pressure field also causes its volume to change; for spherical bubbles this can be described by the Rayleigh-Plesset equation. This means the time-averaged product of the bubble volume and the pressure grad ...
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Bubble (physics)
A bubble is a globule of one substance in another, usually gas in a liquid. Due to the Marangoni effect, bubbles may remain intact when they reach the surface of the immersive substance. Common examples Bubbles are seen in many places in everyday life, for example: * As spontaneous nucleation of supersaturated carbon dioxide in soft drinks * As water vapor in boiling water * As air mixed into agitated water, such as below a waterfall * As sea foam * As a soap bubble * As given off in chemical reactions, e.g., baking soda + vinegar * As a gas trapped in glass during its manufacture * As the indicator in a spirit level Physics and chemistry Bubbles form and coalesce into globular shapes because those shapes are at a lower energy state. For the physics and chemistry behind it, see nucleation. Appearance Bubbles are visible because they have a different refractive index (RI) than the surrounding substance. For example, the RI of air is approximately 1.0003 and the RI of wa ...
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Sound
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the brain. Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans. In air at atmospheric pressure, these represent sound waves with wavelengths of to . Sound waves above 20 kHz are known as ultrasound and are not audible to humans. Sound waves below 20 Hz are known as infrasound. Different animal species have varying hearing ranges. Acoustics Acoustics is the interdisciplinary science that deals with the study of mechanical waves in gasses, liquids, and solids including vibration, sound, ultrasound, and infrasound. A scientist who works in the field of acoustics is an ''acoustician'', while someone working in the field of acoustica ...
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Acoustic Radiation Force
Acoustic radiation force (ARF) is a physical phenomenon resulting from the interaction of an acoustic wave with an obstacle placed along its path. Generally, the force exerted on the obstacle is evaluated by integrating the acoustic radiation pressure (due to the presence of the sonic wave) over its time-varying surface. The magnitude of the force exerted by an acoustic plane wave at any given location can be calculated as: : , F^, = \frac where :*, F^, is a force per unit volume, here expressed in kg/(s2cm2); :*\alpha is the absorption coefficient in Np/cm (Neper/cm); :*I is the temporal average intensity of the acoustic wave at the given location in W/cm2; and :*c is the speed of sound in the medium in cm/s. The effect of frequency on acoustic radiation force is taken into account via intensity (higher pressures are more difficult to attain at higher frequencies) and absorption (higher frequencies have a higher absorption rate). As a reference, water has an acoustic absorp ...
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Vilhelm Bjerknes
Vilhelm Friman Koren Bjerknes ( , ; 14 March 1862 – 9 April 1951) was a Norwegian physicist and meteorologist who did much to found the modern practice of weather forecasting. He formulated the primitive equations that are still in use in numerical weather prediction and climate modeling, and he developed the so-called Bergen School of Meteorology, which was successful in advancing weather prediction and meteorology in the early 20th century. Life and career Born in Christiania (later renamed Oslo), Bjerknes enjoyed an early exposure to fluid dynamics, as assistant to his father, Carl Anton Bjerknes, who had discovered by mathematical analysis the apparent actions at a distance between pulsating and oscillating bodies in a fluid, and their analogy with the electric and magnetic actions at a distance. Apparently no attempt had been made to demonstrate experimentally the theories arrived at by the older professor until Vilhelm Bjerknes, then about 17 or 18 years of age, tur ...
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Travelling Wave
In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a ''traveling wave''; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a ''standing wave''. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero. Waves are often described by a ''wave equation'' (standing wave field of two opposite waves) or a one-way wave equation for single wave propagation in a defined direction. Two types of waves are most commonly studied in classical physics. In a ''mechanical wave'', stress and strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (strain) in so ...
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Minnaert Resonance
The Minnaert resonance is a phenomenon associated with a gas bubble pulsating at its natural frequency in a liquid, neglecting the effects of surface tension and viscous attenuation. It is the frequency of the sound made by a drop of water from a tap falling in water underneath, trapping a bubble of air as it falls. The natural frequency of the entrapped air bubble in the water is given by : f = \cfrac\left(\cfrac\right)^ where a is the radius of the bubble, \gamma is the polytropic coefficient, p_A is the ambient pressure, and \rho is the density of water. This formula can also be used to find the natural frequency of a bubble cloud with a as the radius of the cloud and \rho the difference between the density of water and the bulk density of the cloud. For a single bubble in water at standard pressure (p_A=100~ , ~ \rho=1000~ ), this equation reduces to f a \approx 3.26~m/s , where f~ is the natural frequency of the bubble. The Minnaert formula assumes an ideal gas, how ...
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Standing Wave
In physics, a standing wave, also known as a stationary wave, is a wave that oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with respect to time, and the oscillations at different points throughout the wave are in phase. The locations at which the absolute value of the amplitude is minimum are called nodes, and the locations where the absolute value of the amplitude is maximum are called antinodes. Standing waves were first noticed by Michael Faraday in 1831. Faraday observed standing waves on the surface of a liquid in a vibrating container. Franz Melde coined the term "standing wave" (German: ''stehende Welle'' or ''Stehwelle'') around 1860 and demonstrated the phenomenon in his classic experiment with vibrating strings. This phenomenon can occur because the medium is moving in the direction opposite to the movement of the wave, or it can arise in a stationary medium ...
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Antinode
A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an anti-node, a point where the amplitude of the standing wave is at maximum. These occur midway between the nodes. Explanation Standing waves result when two sinusoidal wave trains of the same frequency are moving in opposite directions in the same space and interfere with each other. They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line, and particularly when waves are confined in a resonator at resonance, bouncing back and forth between two boundaries, such as in an organ pipe or guitar string. In a standing wave the nodes are a seri ...
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Node (physics)
A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an anti-node, a point where the amplitude of the standing wave is at maximum. These occur midway between the nodes. Explanation Standing waves result when two sinusoidal wave trains of the same frequency are moving in opposite directions in the same space and interfere with each other. They occur when waves are reflected at a boundary, such as sound waves reflected from a wall or electromagnetic waves reflected from the end of a transmission line, and particularly when waves are confined in a resonator at resonance, bouncing back and forth between two boundaries, such as in an organ pipe or guitar string. In a standing wave the nodes are a se ...
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Acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an Acoustical engineering, acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries. Hearing (sense), Hearing is one of the most crucial means of survival in the animal world and speech is one of the most distinctive characteristics of human development and culture. Accordingly, the science of acoustics spreads across many facets of human society—music, medicine, architecture, industrial production, warfare and more. Likewise, animal species such as songbirds and frogs use sound and hearing as a key element of mating rituals or for marking territories. Art, ...
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