Cherenkov radiation

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Cherenkov_radiation 

 

Cherenkov radiation glowing in the core of the Advanced Test Reactor.

Cherenkov radiation (/tʃəˈrɛŋkɒf/; Russian: Черенков) is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity (speed of propagation of a wave in a medium) of light in that medium. A classic example of Cherenkov radiation is the characteristic blue glow of an underwater nuclear reactor. Its cause is similar to the cause of a sonic boom, the sharp sound heard when faster-than-sound movement occurs. The phenomenon is named after Soviet physicist Pavel Cherenkov, who shared the 1958 Nobel Prize in Physics for its discovery.

History

The radiation is named after the Soviet scientist Pavel Cherenkov, the 1958 Nobel Prize winner, who was the first to detect it experimentally under the supervision of Sergey Vavilov at the Lebedev Institute in 1934. Therefore, it is also known as Vavilov–Cherenkov radiation. Cherenkov saw a faint bluish light around a radioactive preparation in water during experiments. His doctorate thesis was on luminescence of uranium salt solutions that were excited by gamma rays instead of less energetic visible light, as done commonly. He discovered the anisotropy of the radiation and came to the conclusion that the bluish glow was not a fluorescent phenomenon.

A theory of this effect was later developed in 1937 within the framework of Einstein's special relativity theory by Cherenkov's colleagues Igor Tamm and Ilya Frank, who also shared the 1958 Nobel Prize.

Cherenkov radiation as conical wave front had been theoretically predicted by the English polymath Oliver Heaviside in papers published between 1888 and 1889 and by Arnold Sommerfeld in 1904, but both had been quickly forgotten following the relativity theory's restriction of super-c particles until the 1970s. Marie Curie observed a pale blue light in a highly concentrated radium solution in 1910, but did not investigate its source. In 1926, the French radiotherapist Lucien Mallet described the luminous radiation of radium irradiating water having a continuous spectrum.

In 2019, a team of researchers from Dartmouth’s and Dartmouth-Hitchcock's Norris Cotton Cancer Center discovered Cherenkov light being generated in the vitreous humor of patients undergoing radiotherapy. The light was observed using a camera imaging system called a CDose, which is specially designed to view light emissions from biological systems. For decades, patients had reported phenomena such as “flashes of bright or blue light” when receiving radiation treatments for brain cancer, but the effects had never been experimentally observed.

Physical origin

Basics

While the speed of light in a vacuum is a universal constant (c = 299,792,458 m/s), the speed in a material may be significantly less, as it is perceived to be slowed by the medium. For example, in water it is only 0.75c. Matter can accelerate beyond this speed (although still less than c, the speed of light in vacuum) during nuclear reactions and in particle accelerators. Cherenkov radiation results when a charged particle, most commonly an electron, travels through a dielectric (can be polarized electrically) medium with a speed greater than light's speed in that medium.

The effect can be intuitively described in the following way. From classical physics, it is known that charged particles emit EM waves and via Huygens' principle these waves will form spherical wavefronts which propagate with the phase velocity of that medium (i.e. the speed of light in that medium given by ${\displaystyle c/n}$, for ${\displaystyle n}$, the refractive index). When any charged particle passes through a medium, the particles of the medium will polarize around it in response. The charged particle excites the molecules in the polarizable medium and on returning to their ground state, the molecules re-emit the energy given to them to achieve excitation as photons. These photons form the spherical wavefronts which can be seen originating from the moving particle. If ${\displaystyle v_{p}<c/n}$, that is the velocity of the charged particle is less than that of the speed of light in the medium, then the polarization field which forms around the moving particle is usually symmetric. The corresponding emitted wavefronts may be bunched up but they do not coincide or cross and there are no interference effects to worry about. In the reverse situation, i.e. ${\displaystyle v_{p}>c/n}$, the polarization field is asymmetric along the direction of motion of the particle, as the particles of the medium do not have enough time to recover to their "normal" randomized states. This results in overlapping waveforms (as in the animation) and constructive interference leads to an observed cone-like light signal at a characteristic angle: Cherenkov light.

Animation of Cherenkov radiation

A common analogy is the sonic boom of a supersonic aircraft. The sound waves generated by the aircraft travel at the speed of sound, which is slower than the aircraft, and cannot propagate forward from the aircraft, instead forming a conical shock front. In a similar way, a charged particle can generate a "shock wave" of visible light as it travels through an insulator.

The velocity that must be exceeded is the phase velocity of light rather than the group velocity of light. The phase velocity can be altered dramatically by using a periodic medium, and in that case one can even achieve Cherenkov radiation with no minimum particle velocity, a phenomenon known as the Smith–Purcell effect. In a more complex periodic medium, such as a photonic crystal, one can also obtain a variety of other anomalous Cherenkov effects, such as radiation in a backwards direction (see below) whereas ordinary Cherenkov radiation forms an acute angle with the particle velocity.

Cherenkov radiation in the Reed Research Reactor.

In their original work on the theoretical foundations of Cherenkov radiation, Tamm and Frank wrote,"This peculiar radiation can evidently not be explained by any common mechanism such as the interaction of the fast electron with individual atom or as radiative scattering of electrons on atomic nuclei. On the other hand, the phenomenon can be explained both qualitatively and quantitatively if one takes into account the fact that an electron moving in a medium does radiate light even if it is moving uniformly provided that its velocity is greater than the velocity of light in the medium."

Emission angle

The geometry of the Cherenkov radiation shown for the ideal case of no dispersion.

In the figure on the geometry, the particle (red arrow) travels in a medium with speed ${\displaystyle v_{\text{p}}}$ such that

$${\displaystyle {\frac {c}{n}}<v_{\text{p}}<c,}$$

where ${\displaystyle c}$ is speed of light in vacuum, and ${\displaystyle n}$ is the refractive index of the medium. If the medium is water, the condition is ${\displaystyle 0.75c<v_{\text{p}}<c}$, since ${\displaystyle n\approx 1.33}$ for water at 20 °C.

We define the ratio between the speed of the particle and the speed of light as

$${\displaystyle \beta ={\frac {v_{\text{p}}}{c}}.}$$

The emitted light waves (denoted by blue arrows) travel at speed

$${\displaystyle v_{\text{em}}={\frac {c}{n}}.}$$

The left corner of the triangle represents the location of the superluminal particle at some initial moment (t = 0). The right corner of the triangle is the location of the particle at some later time t. In the given time t, the particle travels the distance

$${\displaystyle x_{\text{p}}=v_{\text{p}}t=\beta \,ct}$$

whereas the emitted electromagnetic waves are constricted to travel the distance

$${\displaystyle x_{\text{em}}=v_{\text{em}}t={\frac {c}{n}}t.}$$

So the emission angle results in

$${\displaystyle \cos \theta ={\frac {1}{n\beta }}}$$

Arbitrary emission angle

Cherenkov radiation can also radiate in an arbitrary direction using properly engineered one dimensional metamaterials. The latter is designed to introduce a gradient of phase retardation along the trajectory of the fast travelling particle (${\displaystyle d\phi /dx}$), reversing or steering Cherenkov emission at arbitrary angles given by the generalized relation:

$${\displaystyle \cos \theta ={\frac {1}{n\beta }}+{\frac {n}{k_{0}}}\cdot {\frac {d\phi }{dx}}}$$

Note that since this ratio is independent of time, one can take arbitrary times and achieve similar triangles. The angle stays the same, meaning that subsequent waves generated between the initial time t = 0 and final time t will form similar triangles with coinciding right endpoints to the one shown.

Reverse Cherenkov effect

A reverse Cherenkov effect can be experienced using materials called negative-index metamaterials (materials with a subwavelength microstructure that gives them an effective "average" property very different from their constituent materials, in this case having negative permittivity and negative permeability). This means that, when a charged particle (usually electrons) passes through a medium at a speed greater than the phase velocity of light in that medium, that particle emits trailing radiation from its progress through the medium rather than in front of it (as is the case in normal materials with, both permittivity and permeability positive). One can also obtain such reverse-cone Cherenkov radiation in non-metamaterial periodic media where the periodic structure is on the same scale as the wavelength, so it cannot be treated as an effectively homogeneous metamaterial.

In a vacuum

The Cherenkov effect can occur in vacuum. In a slow-wave structure, like in a traveling-wave tube (TWT), the phase velocity decreases and the velocity of charged particles can exceed the phase velocity while remaining lower than ${\displaystyle c}$. In such a system, this effect can be derived from conservation of the energy and momentum where the momentum of a photon should be ${\displaystyle p=\hbar \beta }$ (${\displaystyle \beta }$ is phase constant) rather than the de Broglie relation ${\displaystyle p=\hbar k}$. This type of radiation (VCR) is used to generate high-power microwaves.

Characteristics

The frequency spectrum of Cherenkov radiation by a particle is given by the Frank–Tamm formula:

$${\displaystyle {\frac {d^{2}E}{dx\,d\omega }}={\frac {q^{2}}{4\pi }}\mu (\omega )\omega {\left(1-{\frac {c^{2}}{v^{2}n^{2}(\omega )}}\right)}}$$

The Frank–Tamm formula describes the amount of energy ${\displaystyle E}$ emitted from Cherenkov radiation, per unit length traveled ${\displaystyle x}$ and per frequency ${\displaystyle \omega }$. ${\displaystyle \mu (\omega )}$ is the permeability and ${\displaystyle n(\omega )}$ is the index of refraction of the material the charge particle moves through. ${\displaystyle q}$ is the electric charge of the particle, ${\displaystyle v}$ is the speed of the particle, and ${\displaystyle c}$ is the speed of light in vacuum.

Unlike fluorescence or emission spectra that have characteristic spectral peaks, Cherenkov radiation is continuous. Around the visible spectrum, the relative intensity per unit frequency is approximately proportional to the frequency. That is, higher frequencies (shorter wavelengths) are more intense in Cherenkov radiation. This is why visible Cherenkov radiation is observed to be brilliant blue. In fact, most Cherenkov radiation is in the ultraviolet spectrum—it is only with sufficiently accelerated charges that it even becomes visible; the sensitivity of the human eye peaks at green, and is very low in the violet portion of the spectrum.

There is a cut-off frequency above which the equation ${\displaystyle \cos \theta =1/(n\beta )}$ can no longer be satisfied. The refractive index ${\displaystyle n}$ varies with frequency (and hence with wavelength) in such a way that the intensity cannot continue to increase at ever shorter wavelengths, even for very relativistic particles (where v/c is close to 1). At X-ray frequencies, the refractive index becomes less than 1 (note that in media, the phase velocity may exceed c without violating relativity) and hence no X-ray emission (or shorter wavelength emissions such as gamma rays) would be observed. However, X-rays can be generated at special frequencies just below the frequencies corresponding to core electronic transitions in a material, as the index of refraction is often greater than 1 just below a resonant frequency.

As in sonic booms and bow shocks, the angle of the shock cone is directly related to the velocity of the disruption. The Cherenkov angle is zero at the threshold velocity for the emission of Cherenkov radiation. The angle takes on a maximum as the particle speed approaches the speed of light. Hence, observed angles of incidence can be used to compute the direction and speed of a Cherenkov radiation-producing charge.

Cherenkov radiation can be generated in the eye by charged particles hitting the vitreous humour, giving the impression of flashes, as in cosmic ray visual phenomena and possibly some observations of criticality accidents.

Uses

Detection of labelled biomolecules

Cherenkov radiation is widely used to facilitate the detection of small amounts and low concentrations of biomolecules. Radioactive atoms such as phosphorus-32 are readily introduced into biomolecules by enzymatic and synthetic means and subsequently may be easily detected in small quantities for the purpose of elucidating biological pathways and in characterizing the interaction of biological molecules such as affinity constants and dissociation rates.

Medical imaging of radioisotopes and external beam radiotherapy

Cherenkov light emission imaged from the chest wall of a patient undergoing whole breast irradiation, using 6 MeV beam from a linear accelerator in radiotherapy.

More recently, Cherenkov light has been used to image substances in the body. These discoveries have led to intense interest around the idea of using this light signal to quantify and/or detect radiation in the body, either from internal sources such as injected radiopharmaceuticals or from external beam radiotherapy in oncology. Radioisotopes such as the positron emitters ¹⁸F and ¹³N or beta emitters ³²P or ⁹⁰Y have measurable Cherenkov emission and isotopes ¹⁸F and ¹³¹I have been imaged in humans for diagnostic value demonstration. External beam radiation therapy has been shown to induce a substantial amount of Cherenkov light in the tissue being treated, due to the photon beam energy levels used in the 6 MeV to 18 MeV ranges. The secondary electrons induced by these high energy x-rays result in the Cherenkov light emission, where the detected signal can be imaged at the entry and exit surfaces of the tissue.

Nuclear reactors

Cherenkov radiation in a TRIGA reactor pool.

Cherenkov radiation is used to detect high-energy charged particles. In open pool reactors, beta particles (high-energy electrons) are released as the fission products decay. The glow continues after the chain reaction stops, dimming as the shorter-lived products decay. Similarly, Cherenkov radiation can characterize the remaining radioactivity of spent fuel rods. This phenomenon is used to verify the presence of spent nuclear fuel in spent fuel pools for nuclear safeguards purposes.

Astrophysics experiments

When a high-energy (TeV) gamma photon or cosmic ray interacts with the Earth's atmosphere, it may produce an electron-positron pair with enormous velocities. The Cherenkov radiation emitted in the atmosphere by these charged particles is used to determine the direction and energy of the cosmic ray or gamma ray, which is used for example in the Imaging Atmospheric Cherenkov Technique (IACT), by experiments such as VERITAS, H.E.S.S., MAGIC. Cherenkov radiation emitted in tanks filled with water by those charged particles reaching earth is used for the same goal by the Extensive Air Shower experiment HAWC, the Pierre Auger Observatory and other projects. Similar methods are used in very large neutrino detectors, such as the Super-Kamiokande, the Sudbury Neutrino Observatory (SNO) and IceCube. Other projects operated in the past applying related techniques, such as STACEE, a former solar tower refurbished to work as a non-imaging Cherenkov observatory, which was located in New Mexico.

Astrophysics observatories using the Cherenkov technique to measure air showers are key to determine the properties of astronomical objects that emit Very High Energy gamma rays, such as supernova remnants and blazars.

Particle physics experiments

See also: Cherenkov detector and Ring imaging Cherenkov detector

Cherenkov radiation is commonly used in experimental particle physics for particle identification. One could measure (or put limits on) the velocity of an electrically charged elementary particle by the properties of the Cherenkov light it emits in a certain medium. If the momentum of the particle is measured independently, one could compute the mass of the particle by its momentum and velocity (see four-momentum), and hence identify the particle.

The simplest type of particle identification device based on a Cherenkov radiation technique is the threshold counter, which answers whether the velocity of a charged particle is lower or higher than a certain value (${\displaystyle v_{0}=c/n}$, where ${\displaystyle c}$ is the speed of light, and ${\displaystyle n}$ is the refractive index of the medium) by looking at whether this particle emits Cherenkov light in a certain medium. Knowing particle momentum, one can separate particles lighter than a certain threshold from those heavier than the threshold.

The most advanced type of a detector is the RICH, or ring-imaging Cherenkov detector, developed in the 1980s. In a RICH detector, a cone of Cherenkov light is produced when a high-speed charged particle traverses a suitable medium, often called radiator. This light cone is detected on a position sensitive planar photon detector, which allows reconstructing a ring or disc, whose radius is a measure for the Cherenkov emission angle. Both focusing and proximity-focusing detectors are in use. In a focusing RICH detector, the photons are collected by a spherical mirror and focused onto the photon detector placed at the focal plane. The result is a circle with a radius independent of the emission point along the particle track. This scheme is suitable for low refractive index radiators—i.e. gases—due to the larger radiator length needed to create enough photons. In the more compact proximity-focusing design, a thin radiator volume emits a cone of Cherenkov light which traverses a small distance—the proximity gap—and is detected on the photon detector plane. The image is a ring of light whose radius is defined by the Cherenkov emission angle and the proximity gap. The ring thickness is determined by the thickness of the radiator. An example of a proximity gap RICH detector is the High Momentum Particle Identification Detector (HMPID), a detector currently under construction for ALICE (A Large Ion Collider Experiment), one of the six experiments at the LHC (Large Hadron Collider) at CERN.

Sonic boom

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Sonic_boom 

The sound source is travelling at 1.4 times the speed of sound (Mach 1.4). Since the source is moving faster than the sound waves it creates, it leads the advancing wavefront.

 

A sonic boom produced by an aircraft moving at M=2.92, calculated from the cone angle of 20 degrees. Observers hear nothing until the shock wave, on the edges of the cone, crosses their location.

 

Mach cone angle

 

NASA data showing N-wave signature.

 

Conical shockwave with its hyperbola-shaped ground contact zone in yellow

A sonic boom is a sound associated with shock waves created when an object travels through the air faster than the speed of sound. Sonic booms generate enormous amounts of sound energy, sounding similar to an explosion or a thunderclap to the human ear. The crack of a supersonic bullet passing overhead or the crack of a bullwhip are examples of a sonic boom in miniature.

Sonic booms due to large supersonic aircraft can be particularly loud and startling, tend to awaken people, and may cause minor damage to some structures. They led to prohibition of routine supersonic flight over land. Although they cannot be completely prevented, research suggests that with careful shaping of the vehicle, the nuisance due to the sonic booms may be reduced to the point that overland supersonic flight may become a feasible option.

A sonic boom does not occur only at the moment an object crosses the speed of sound; and neither is it heard in all directions emanating from the supersonic object. Rather the boom is a continuous effect that occurs while the object is travelling at supersonic speeds. But it affects only observers that are positioned at a point that intersects a region in the shape of a geometrical cone behind the object. As the object moves, this conical region also moves behind it and when the cone passes over the observer, they will briefly experience the boom.

Causes

When an aircraft passes through the air, it creates a series of pressure waves in front of the aircraft and behind it, similar to the bow and stern waves created by a boat. These waves travel at the speed of sound and, as the speed of the object increases, the waves are forced together, or compressed, because they cannot get out of each other's way quickly enough. Eventually they merge into a single shock wave, which travels at the speed of sound, a critical speed known as Mach 1, and is approximately 1,235 km/h (767 mph) at sea level and 20 °C (68 °F).

In smooth flight, the shock wave starts at the nose of the aircraft and ends at the tail. Because the different radial directions around the aircraft's direction of travel are equivalent (given the "smooth flight" condition), the shock wave forms a Mach cone, similar to a vapour cone, with the aircraft at its tip. The half-angle ${\displaystyle \alpha }$ between the direction of flight and the shock wave is given by:

${\displaystyle \sin(\alpha )={\frac {v_{\text{sound}}}{v_{\text{object}}}}}$,

where ${\displaystyle {\frac {v_{\text{sound}}}{v_{\text{object}}}}}$ is the inverse ${\displaystyle {\Big (}{\frac {1}{Ma}}{\Big )}}$ of the plane's Mach number (${\displaystyle Ma={\frac {v_{\text{object}}}{v_{\text{sound}}}}}$). Thus the faster the plane travels, the finer and more pointed the cone is.

There is a rise in pressure at the nose, decreasing steadily to a negative pressure at the tail, followed by a sudden return to normal pressure after the object passes. This "overpressure profile" is known as an N-wave because of its shape. The "boom" is experienced when there is a sudden change in pressure; therefore, an N-wave causes two booms – one when the initial pressure-rise reaches an observer, and another when the pressure returns to normal. This leads to a distinctive "double boom" from a supersonic aircraft. When the aircraft is maneuvering, the pressure distribution changes into different forms, with a characteristic U-wave shape.

Since the boom is being generated continually as long as the aircraft is supersonic, it fills out a narrow path on the ground following the aircraft's flight path, a bit like an unrolling red carpet, and hence known as the boom carpet. Its width depends on the altitude of the aircraft. The distance from the point on the ground where the boom is heard to the aircraft depends on its altitude and the angle ${\displaystyle \alpha }$.

For today's supersonic aircraft in normal operating conditions, the peak overpressure varies from less than 50 to 500 Pa (1 to 10 psf (pound per square foot)) for an N-wave boom. Peak overpressures for U-waves are amplified two to five times the N-wave, but this amplified overpressure impacts only a very small area when compared to the area exposed to the rest of the sonic boom. The strongest sonic boom ever recorded was 7,000 Pa (144 psf) and it did not cause injury to the researchers who were exposed to it. The boom was produced by an F-4 flying just above the speed of sound at an altitude of 100 feet (30 m). In recent tests, the maximum boom measured during more realistic flight conditions was 1,010 Pa (21 psf). There is a probability that some damage — shattered glass, for example — will result from a sonic boom. Buildings in good condition should suffer no damage by pressures of 530 Pa (11 psf) or less. And, typically, community exposure to sonic boom is below 100 Pa (2 psf). Ground motion resulting from sonic boom is rare and is well below structural damage thresholds accepted by the U.S. Bureau of Mines and other agencies.

The power, or volume, of the shock wave depends on the quantity of air that is being accelerated, and thus the size and shape of the aircraft. As the aircraft increases speed the shock cone gets tighter around the craft and becomes weaker to the point that at very high speeds and altitudes no boom is heard. The "length" of the boom from front to back depends on the length of the aircraft to a power of 3/2. Longer aircraft therefore "spread out" their booms more than smaller ones, which leads to a less powerful boom.

Several smaller shock waves can and usually do form at other points on the aircraft, primarily at any convex points, or curves, the leading wing edge, and especially the inlet to engines. These secondary shockwaves are caused by the air being forced to turn around these convex points, which generates a shock wave in supersonic flow.

The later shock waves are somewhat faster than the first one, travel faster and add to the main shockwave at some distance away from the aircraft to create a much more defined N-wave shape. This maximizes both the magnitude and the "rise time" of the shock which makes the boom seem louder. On most aircraft designs the characteristic distance is about 40,000 feet (12,000 m), meaning that below this altitude the sonic boom will be "softer". However, the drag at this altitude or below makes supersonic travel particularly inefficient, which poses a serious problem.

Measurement and examples

The pressure from sonic booms caused by aircraft is often a few pounds per square foot. A vehicle flying at greater altitude will generate lower pressures on the ground, because the shock wave reduces in intensity as it spreads out away from the vehicle, but the sonic booms are less affected by vehicle speed.

Aircraft	Speed	Altitude	Pressure (lbf/ft2)	Pressure (Pa)
SR-71 Blackbird	Mach 3+	80,000 feet (24,000 m)	0.9	43
Concorde (SST)	Mach 2	52,000 feet (16,000 m)	1.94	93
F-104 Starfighter	Mach 1.93	48,000 feet (15,000 m)	0.8	38
Space Shuttle	Mach 1.5	60,000 feet (18,000 m)	1.25	60

Abatement

New research is being performed at NASA's Glenn Research Center that could help alleviate the sonic boom produced by supersonic aircraft. Testing was completed in 2010 of a Large-Scale Low-Boom supersonic inlet model with micro-array flow control. A NASA aerospace engineer is pictured here in a wind tunnel with the Large-Scale Low-Boom supersonic inlet model.

In the late 1950s when supersonic transport (SST) designs were being actively pursued, it was thought that although the boom would be very large, the problems could be avoided by flying higher. This assumption was proven false when the North American XB-70 Valkyrie first flew, and it was found that the boom was a problem even at 70,000 feet (21,000 m). It was during these tests that the N-wave was first characterized.

Richard Seebass and his colleague Albert George at Cornell University studied the problem extensively and eventually defined a "figure of merit" (FM) to characterize the sonic boom levels of different aircraft. FM is a function of the aircraft weight and the aircraft length. The lower this value, the less boom the aircraft generates, with figures of about 1 or lower being considered acceptable. Using this calculation, they found FMs of about 1.4 for Concorde and 1.9 for the Boeing 2707. This eventually doomed most SST projects as public resentment, mixed with politics, eventually resulted in laws that made any such aircraft less useful (flying supersonically only over water for instance). Small aeroplane designs like business jets are favoured and tend to produce minimal to no audible booms.

Seebass and George also worked on the problem from a different angle, trying to spread out the N-wave laterally and temporally (longitudinally), by producing a strong and downwards-focused (SR-71 Blackbird, Boeing X-43) shock at a sharp, but wide angle nose cone, which will travel at slightly supersonic speed (bow shock), and using a swept back flying wing or an oblique flying wing to smooth out this shock along the direction of flight (the tail of the shock travels at sonic speed). To adapt this principle to existing planes, which generate a shock at their nose cone and an even stronger one at their wing leading edge, the fuselage below the wing is shaped according to the area rule. Ideally this would raise the characteristic altitude from 40,000 feet (12,000 m) to 60,000 feet (from 12,000 m to 18,000 m), which is where most SST aircraft were expected to fly.

 

NASA F-5E modified for DARPA sonic boom tests

This remained untested for decades, until DARPA started the Quiet Supersonic Platform project and funded the Shaped Sonic Boom Demonstration (SSBD) aircraft to test it. SSBD used an F-5 Freedom Fighter. The F-5E was modified with a highly refined shape which lengthened the nose to that of the F-5F model. The fairing extended from the nose all the way back to the inlets on the underside of the aircraft. The SSBD was tested over a two-year period culminating in 21 flights and was an extensive study on sonic boom characteristics. After measuring the 1,300 recordings, some taken inside the shock wave by a chase plane, the SSBD demonstrated a reduction in boom by about one-third. Although one-third is not a huge reduction, it could have reduced Concorde's boom to an acceptable level below FM = 1.

As a follow-on to SSBD, in 2006 a NASA-Gulfstream Aerospace team tested the Quiet Spike on NASA-Dryden's F-15B aircraft 836. The Quiet Spike is a telescoping boom fitted to the nose of an aircraft specifically designed to weaken the strength of the shock waves forming on the nose of the aircraft at supersonic speeds. Over 50 test flights were performed. Several flights included probing of the shockwaves by a second F-15B, NASA's Intelligent Flight Control System testbed, aircraft 837.

There are theoretical designs that do not appear to create sonic booms at all, such as the Busemann biplane. However, creating a shockwave is inescapable if they generate aerodynamic lift.

NASA and Lockheed Martin Aeronautics Co. are working together to build an experimental aircraft called the Low Boom Flight Demonstrator (LBFD), which will reduce the sonic boom synonymous with high-speed flight to the sound of a car door closing. The agency has awarded a $247.5 million contract to construct a working version of the sleek, single-pilot plane by summer 2021 and should begin testing over the following years to determine whether the design could eventually be adapted to commercial aircraft.

Perception, noise and other concerns

A point source emitting spherical fronts while increasing its velocity linearly with time. For short times the Doppler effect is visible. When v = c, the sonic boom is visible. When v > c, the Mach cone is visible.

The sound of a sonic boom depends largely on the distance between the observer and the aircraft shape producing the sonic boom. A sonic boom is usually heard as a deep double "boom" as the aircraft is usually some distance away. The sound is much like that of mortar bombs, commonly used in firework displays. It is a common misconception that only one boom is generated during the subsonic to supersonic transition; rather, the boom is continuous along the boom carpet for the entire supersonic flight. As a former Concorde pilot puts it, "You don't actually hear anything on board. All we see is the pressure wave moving down the aeroplane – it gives an indication on the instruments. And that's what we see around Mach 1. But we don't hear the sonic boom or anything like that. That's rather like the wake of a ship – it's behind us."

In 1964, NASA and the Federal Aviation Administration began the Oklahoma City sonic boom tests, which caused eight sonic booms per day over a period of six months. Valuable data was gathered from the experiment, but 15,000 complaints were generated and ultimately entangled the government in a class-action lawsuit, which it lost on appeal in 1969.

Sonic booms were also a nuisance in North Cornwall and North Devon in the UK as these areas were underneath the flight path of Concorde. Windows would rattle and in some cases the "torching" (pointing underneath roof slates) would be dislodged with the vibration.

There has been recent work in this area, notably under DARPA's Quiet Supersonic Platform studies. Research by acoustics experts under this program began looking more closely at the composition of sonic booms, including the frequency content. Several characteristics of the traditional sonic boom "N" wave can influence how loud and irritating it can be perceived by listeners on the ground. Even strong N-waves such as those generated by Concorde or military aircraft can be far less objectionable if the rise time of the over-pressure is sufficiently long. A new metric has emerged, known as perceived loudness, measured in PLdB. This takes into account the frequency content, rise time, etc. A well-known example is the snapping of one's fingers in which the "perceived" sound is nothing more than an annoyance.

The energy range of sonic boom is concentrated in the 0.1–100 hertz frequency range that is considerably below that of subsonic aircraft, gunfire and most industrial noise. Duration of sonic boom is brief; less than a second, 100 milliseconds (0.1 second) for most fighter-sized aircraft and 500 milliseconds for the space shuttle or Concorde jetliner. The intensity and width of a sonic boom path depends on the physical characteristics of the aircraft and how it is operated. In general, the greater an aircraft's altitude, the lower the over-pressure on the ground. Greater altitude also increases the boom's lateral spread, exposing a wider area to the boom. Over-pressures in the sonic boom impact area, however, will not be uniform. Boom intensity is greatest directly under the flight path, progressively weakening with greater horizontal distance away from the aircraft flight track. Ground width of the boom exposure area is approximately 1 statute mile (1.6 km) for each 1,000 feet (300 m) of altitude (the width is about five times the altitude); that is, an aircraft flying supersonic at 30,000 feet (9,100 m) will create a lateral boom spread of about 30 miles (48 km). For steady supersonic flight, the boom is described as a carpet boom since it moves with the aircraft as it maintains supersonic speed and altitude. Some maneuvers, diving, acceleration or turning, can cause focusing of the boom. Other maneuvers, such as deceleration and climbing, can reduce the strength of the shock. In some instances weather conditions can distort sonic booms.

Depending on the aircraft's altitude, sonic booms reach the ground 2 to 60 seconds after flyover. However, not all booms are heard at ground level. The speed of sound at any altitude is a function of air temperature. A decrease or increase in temperature results in a corresponding decrease or increase in sound speed. Under standard atmospheric conditions, air temperature decreases with increased altitude. For example, when sea-level temperature is 59 degrees Fahrenheit (15 °C), the temperature at 30,000 feet (9,100 m) drops to minus 49 degrees Fahrenheit (−45 °C). This temperature gradient helps bend the sound waves upward. Therefore, for a boom to reach the ground, the aircraft speed relative to the ground must be greater than the speed of sound at the ground. For example, the speed of sound at 30,000 feet (9,100 m) is about 670 miles per hour (1,080 km/h), but an aircraft must travel at least 750 miles per hour (1,210 km/h) (Mach 1.12) for a boom to be heard on the ground.

The composition of the atmosphere is also a factor. Temperature variations, humidity, atmospheric pollution, and winds can all have an effect on how a sonic boom is perceived on the ground. Even the ground itself can influence the sound of a sonic boom. Hard surfaces such as concrete, pavement, and large buildings can cause reflections which may amplify the sound of a sonic boom. Similarly, grassy fields and profuse foliage can help attenuate the strength of the over-pressure of a sonic boom.

Currently there are no industry-accepted standards for the acceptability of a sonic boom. However, work is underway to create metrics that will help in understanding how humans respond to the noise generated by sonic booms.  Until such metrics can be established, either through further study or supersonic overflight testing, it is doubtful that legislation will be enacted to remove the current prohibition on supersonic overflight in place in several countries, including the United States.

Bullwhip

An Australian bullwhip

The cracking sound a bullwhip makes when properly wielded is, in fact, a small sonic boom. The end of the whip, known as the "cracker", moves faster than the speed of sound, thus creating a sonic boom.

A bullwhip tapers down from the handle section to the cracker. The cracker has much less mass than the handle section. When the whip is sharply swung, the energy is transferred down the length of the tapering whip. Goriely and McMillen showed that the physical explanation is complex, involving the way that a loop travels down a tapered filament under tension.