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Beginning the Acoustic Guitar

admin — Sat, 04 Feb 2012 19:34:28 +0000

Ever looked at your guitar and wanted to throw it in the bin?

I’ve been there! I know exactly how you feel, believe me! There are times I want to scream in frustration because my fingers will not do what my brain is so blatantly telling them to do!

But then, I’ve been playing for years and sometimes I still get that. I still sometimes feel like I could throw my guitar out of the window. But I never have. The reason? Well because I love music and believe that harming a musical instrument is something akin to sacrilege. Sad I know, but then, thats me.

Mentality

To begin playing guitar, you must approach it with the same mindset as you do your career. To do well and succeed, I must work hard, while at the same time, I must have fun! Remember that playing guitar is not all about work. Sometimes it’s nice just to pick up your guitar and lazily strum a few songs, be it alone, or with your friends.

Practice

Practice makes perfect.

Yes it does. That old cliche was repeated to me by my teacher time and again. Work the scales, work the scales, she used to say. But the reasoning became clear after only a couple of weeks (even though she carried on telling me for years!). When you have practiced scales for a couple of weeks, you will find that the first ones you started with are imprinted in your mind, much like your computer login information. It just sticks.

Don’t Give Up!

If you are finding it difficult to master a particular scale or exercise, put the guitar down. Go and have a rest. Watch TV or something for an hour. But come back to it the same day! You’ll be so glad you did. Do NOT give up at this stage. This is the grounding for the rest of your guitar playing life, believe me. This is how nearly every other guitarist I know has done so well. They didn’t give up.

Warm-ups

An important part of any guitar session is warming up. You can do this by running scales, using hand grips, or even just messing about on your guitar! The reason you need to warm up is that your movements will be much more fluid and the benefit will be noticeable instantly through greater mobility over the fretboard.

Closing advice

The best piece of advice I can give you is “get a teacher!”. It’s worth it, believe me. You will avoid the traps I fell into before I got one. I had all kinds of bad habits, like spanning when I shouldn’t, using incorrect phrases, anchoring the little finger of my picking hand to the guitar, and the list went on! Getting a teacher will get you out of all of this, and will be well worth the investment, because there are two very very valuable things you will gain: Solid Technique and Enjoyment. The holy grail for any guitarist! I hope you get there, I seriously do!

Thats all for now, and I wish you every success in your musical future.

Let’s Make the Shipment Easier

admin — Sat, 04 Feb 2012 02:58:08 +0000

For product providers, shipment system becomes important since it will give them such a great impression toward their customers. If they deliver the products on time, they will get their customer’s satisfaction. It will give good impact to their business since there is a big chance for the customers to reorder their product. However, it is not an easy thing to handle this matter. It needs careful attention since the goods to be shipped are in a big quantity.

If you think that you are incapable of handling the goods, you may ask for help for this matter. Drop360.com offers you a great service in handling your goods. They are a company running a business in ecommerce fulfillment services . They give you shipping service for all over the world. Their fulfillment services provide customers with such a great service before the goods are being shipped.

Another great thing offered by this company is called drop ship ecommerce and shipping fulfillment position . This will help you much for shipping your products to your consumers whenever they are. So, when you need trusted company to help you handling your product shipment, please make sure that you visit the website mentioned. Try their service now.

Taylor Acoustic Guitar Information

admin — Sat, 04 Feb 2012 02:33:44 +0000

When people hear the word guitar, they may think of brands such as Ibanez, Fender, Gibson, Yamaha, and Martin. However, the Taylor acoustic guitar is one of the most popular and best sounding guitars on the market today. If you have ever played or heard one yourself, you know exactly what I am talking about.

The Taylor acoustic guitar was created by Bob Taylor back in 1974, when he was only 19 years old. At that time, he was working for a guitar manufacturer called American Dream. When the owner of that company decided to sell, Bob Taylor jumped on the opportunity as fast as he could, knowing that the guitar industry is where he wanted to continue his work. He named the company Westland Music Company (because it was located in the western United States.

Nowadays, there are two factories in which a Taylor acoustic guitar is created, run by around 550 employees total: one in El Cajon, California, and the other in Tecate, Mexico.

Taylor does manufacture a few solid body electric guitars, but their main focus is on acoustic guitars.

There are currently several series of Taylor acoustic guitar available on the market today, from the 3-series through the 8-series, as well as the 810/910 and LKSM models. These guitars are available in four different styles, including dreadnought, grand concert, grand auditorium, and grand symphony.

One aspect of the guitar creation business that Taylor prides itself in is high quality workmanship, which is only rivaled by their top competitor, Martin Guitars. Most of Taylor’s Guitars are made in their El Cajon shop, and the smaller models are built in the Tecate, Mexico shop.

Being such a leader in the industry, not only is the Taylor acoustic guitar the perfect place to start for the beginning guitar player, it is great for the expert as well.

Though there is no “perfect guitar” for any one person, the Taylor is a great place to start. When you begin looking for guitars, make sure you play a few different brands (including Taylor of course!) to get a good idea of how each one sounds. You will certainly notice a difference in tone and quality of sound between the Taylor and lower-end models.

Keep in mind that a Taylor acoustic guitar costs a little bit more money for a reason. They are of great quality and will last forever if it is taken good care of. The cost of one is anywhere between 0 for lower-end and Baby models, and can go upwards of 00 for the high-end series of guitars, such as Taylor’s Koa.

Your job now is to continue to do some searching and playing to see which Taylor acoustic guitar is right for you. After some time of testing and playing, you will soon find one that fits you best, and you will become the proud owner of a new Taylor!

Tony McGuigano is the owner of the Taylor Acoustic Guitar website, as well as a website called Philadelphia Mortgage.

Top Rated Male Enlargement Vitamins

admin — Sat, 04 Feb 2012 02:10:08 +0000

Today, all things can be available on the internet. It seems that people will start to open their mind about the existence of the internet as another side of their life. It is because some activities which are usually done in the real world have been also done on the internet as the cyber world. One visible activity is shopping. For certain years ago, people will go to the nearest store to go shopping but it will not work like that again. It is because they will only need to open their connection through the internet, and they will be able to get all they want to buy there.

Male is only a part of society who will be profitable in which the existence of the internet provides top rated male enlargement vitamins, accessible market to buy sex attributes including sex toy, sex pill, and so forth. It means that they do not need to go to stores and find the fact that the sex toys are out of stock or something. It is because they can get all their needs such as top rated natural penis enhancement through the internet.

One of some sex attributes which are often ordered by males is pills for male enhancement. The pills function as penis enhancement in which they can improve their penis size as well as their sex performance. Besides, you can also get male enhancement cage through appropriate website like Sinrex.

Extending the Size with the Extender

admin — Sat, 04 Feb 2012 02:03:00 +0000

There are some men who don’t feel confidence about their size and wish that they have bigger size. They are willing to get through several treatments in order to get the bigger size. A lot of men think that their size is one of the most important things in their sex activities; therefore they try to get the bigger size by several treatments that they think to be the most helpful. They can use the traditional treatments or prefer the modern treatments. Most people will go with the modern treatment such as using the penis enlargement that are available in several options.

These men who do not have enough confidence in their size or their performance in the sexual activities may use the enhancement devices. They can use the enhancement pills or supplements or the enlargement pills. They can also choose to use the penis extender or the penis pump are that intended for the same purpose of enlarge the size of their penis. A lot of men have used these devices and satisfied with the results given by these devices. The results may vary according to the quality of the devices used by the men. Check out this site now.

Overcome Your Financial Problems Quickly

alex — Fri, 03 Feb 2012 15:27:32 +0000

Life is sometimes cruel to us. That’s what some people think when they are in their lowest point due to problems they face. However, we should not think that life is cruel just because we face financial difficulties. We do not face financial difficulties all the time, don’t we? It is just that we need more for today since we have more to do. Other people also often face the same circumstance with us. Financial difficulties have become common problem in human life.

To overcome the problem, people who concern with the problem see it as a chance to help people with financial difficulties. These people understand that sometimes people cannot wait to get cash they need due to the urgency they face. Thus, they make effort to improve their approval process and the fastest way to get cash fast is by getting payday loans online so far.

Since the loans offer fast process of approving each application they do not do deeper investigation. Hence, they do not bother to find out our credit score. They never count it as one consideration to determine whether you deserve the loan or not. People with bad credit do not need to worry to get loans anymore since they are also a kind of bad credit loans. It can be concluded that payday loans are suitable for everyone.

Does Vigrx Plus Work? An Independent Vigrx Plus Review

admin — Fri, 03 Feb 2012 04:15:42 +0000

The most popular question asked by individuals is whether Vigrx Plus really works. Accordingly, people look through all the Vigrx Plus reviews to answer the question of whether Vigrx Plus really works. Sadly, many men are not pleased about the size of their penis.

Men have been trying to find ways to make their penis bigger for many years. Take a look at this Vigrx Plus review to determine whether you will benefit from purchasing this product. Vigrx Plus is considered the best supplement ever because of its innovative design. Bioperin contains natural ingredients with a new herb.

Once this herb is mixed with the remaining nutrients, it enhances their rate of absorption.

A full understanding of how your penis works may be essential if you really want to use Vigrx Plus. Consequently, this will aid your ability to understand the way this product achieves an effect.

Your penis consists of three separate cylinders, with two of them being referred to as the Corpora Cavernous. This is the anatomy that allows the penis to fill with blood, creating the erection. Once blood flow has reached maximum capacity, the erection is at its fullest.

Corpusspongiosum is the scientific term for the third tube that comprises the male genitalia. This reference is to the area of the penis where ejaculate is released. When we check the details related to Vigrx plus, the Corpora Caver nose answers the herbs which strengthen, and thus, with the right mix of herbs, the cylinders may settle in better capacity.

According to both doctors and its manufacturers, using this product will increase the size of the penis, sexual stamina, circulation and virility. According some of the reviews given for VigRX, the product will increase the blood movement to the penis without negatively impacting an individual’s blood pressure. Your penis health can be accentuated by relaxing your nervous system.

Don’t worry, herbal supplements supply superior results in a short amount of time. You will begin to become aware that you have both a more intense erection and a bigger penis.

At first your penis will become wider, and then a few dramatic changes in your appearance will occur. There will be a noticeable improvement in all areas of your penis. You will feel more confident in your man hood during sexual situations.

Silent Disco, the Disco Killer?

admin — Tue, 31 Jan 2012 06:16:16 +0000

An event surroundings for people that desire to dance along with listen to high decibel tunes while those wanting to chitchat as well as relax, might do so and never having to raise your voice to be heard. Welcome to the Silent Disco!

It really is as much fun to watch as it’s to take part, given that everybody’s dancing to their own beat. Individuals who stumble upon a Silent Disco can’t even conceptualize what the heck is taking place as they see men and women dancing around and they will not hear anything. A person dancing to electro along with other to swing, it’s very strange and you risk having a laugh on your face.

The headset concept encourages much more talk as well. Dancers may take their own earphones off (or turn down the sound level) at will to have a chat with somebody, and the lack of a sound system means they could actually hear each other. On a typical dance floor, every person stays in their small circles but at Silent Disco, there is certainly a lot more conversation between people.

Picture this: you walk into a room, there’s no music playing and the only sound is that of people dancing around and sometimes singing along to a song that can you cannot hear yourself. There is definitely something wrong with that picture but as soon as you grab a pair of headphones everything becomes clear.

‘You get a really good vibe from people who are listening to the same channel as you so if you see some people dancing or singing along to something, you can ask them what channel they’re on and they put up their fingers, ‘Two’ or ‘Three’ and you switch over and start singing along and kind of feel a part of the group that’s on the one channel,’ said Bascom. ‘You can also just take your headphones off and talk to the person next to you in a regular voice.’

Absolutely no noise complaints, absolutely no issues! The Silent Disco permits the show to run right up until the early hours of the day with minimum disruption to neighbors.

Acoustic Seals

admin — Wed, 25 Jan 2012 17:23:18 +0000

Acoustic seals are a form of door seal that are designed primarily to prevent the passage of noise into or out of a room. They work by sealing off air gaps so that the noise is unable to pass through any open gaps. One of the beneficial side effects of having acoustic seals installed in your home is that they also prevent the passage of dirt, dust, and even smoke through the same gaps. Acoustic seals can be used in residential, commercial, and retail properties to great effect.

Sound Escape

Sound is most commonly lost through the door seal around the top, bottom, and sides of a door. Even the slightest gap that is left allows sound to travel from one area to another and without adequate sealing this will continue to be the case. No amount of soundproofing in the room, under the floors, or anywhere else around the area will fully prevent the escape or entry of noise.

How Acoustic Seals Work

Seals basically form a solid boundary between the door and the door frame. This seal acts in the same way as the walls in which the door is located preventing not only sound but light, smoke, dust, and more from passing from one room to another or from one area to another.

How Much Sound Will They Prevent?

Acoustic seals will typically come with a decibel rating. This means that the seal has been tested and proven to block sounds up to the given decibel level. Its possible to cut out noises up to 34dB with some seals while others have been tested against noise up to 42dB in level. Typically, the greater the protection, the thicker the seal is with some seals as thin as 5mm and others considerably thicker.

Acoustic Seals

Acoustic seals have excellent value in residential properties. In blocks of flats this can prevent noise traveling from one flat to another and can reduce the noise pollution that a flat endures thanks to the communal hallway or other communal areas. Shops can use acoustic seals to prevent noise getting in while certain shops can use the same acoustic seals to prevent noise from escaping and annoying neighbouring buildings.

Acoustic Metamaterials

admin — Fri, 20 Jan 2012 22:05:30 +0000

History of the acoustic metamaterials

Acoustic metamaterials actually began with electromagnetic metamaterials, and the construction of materials to control electromagnetic radiation before that.

Maxwell’s equations which predicted the existence of electromagnetic radiation propagating at the speed of light, by James Clerk Maxwell, were made public in 1865. In 1888 Hertz had demonstrated generation of electromagnetic waves, and showed that their properties were similar to those of light.

Before the start of the twentieth century, many of the concepts now familiar in microwaves had been developed. The list includes the cylindrical parabolic reflector, dielectric lens, microwave absorbers, the cavity radiator, the radiating iris and the pyramidal electromagnetic horn. Round square and rectangular waveguides were used, with experimental development anticipating by several years Rayleigh’s 1896 theoretical solution for waveguide modes.

Many microwave components in use were “quasi-optical”. Oliver Lodge first introduced the term – quasi-optical. A treatise on microwave optics was published by Righi in 1897.

Hertz had used a wavelength of 66 cm; other post-Hertzian pre-1900 experimenters used wavelengths well into the short cm-wave region, with Bose in Calcutta and Lebedew in Moscow independently performing experiments at wavelengths as short as 5 and 6 milimeters.

Jagadish Chandra Bose used waveguides, horn antennas, dielectric lenses, various polarizers and even semiconductors at frequencies as high as 60 GHz. In 1898 he tried to develop and did experiments with “constructed” twisted elements.

These elements exhibited chiral properties. He authored a paper, published by Proceedings Royal Society London on January 1, 1898 “On the Rotation of Plane of Polarisation of Electric Waves by a Twisted Structure”.

In the early part of the twentieth century, Karl Ferdinand Lindman studied wave interaction with collections of metallic helices as artificial chiral media (Annalen der Physik, Vol. 63, No. 4, pp. 621644, 1920.)

W. E. Kock developed materials that had similar characteristics to metamaterials in the late 1940s Winkler (1956), Tinoco and Freeman (1957), W. Pickering 1970, Several Groups in 1980 and 1990.

The modern form of metamaterials was originally proposed by Victor G. Veselago, in 1967. Microwave LH Media domain – Negative refraction (electromagnetic) first demonstrated by D. Smith, S. Shultz, and R. Shelby (20002001) Anomalous refraction in DNG Media leads to Pendry’s perfect lens proposal (evanescent wave reconstruction). Paired layers of metamaterials with negative permittivity and permeability (DNG) and conventional materials (DPS) follow.

In the year 2000 sonic (rubber-silicon coated) crystals in liquid result in the first acoustic metamaterial.

The research on acoustic metamaterials began in the year 2000 with the fabrication and demonstration of sonic crystals in a liquid. This was followed by transposing the behavior of the split-ring resonator to research in acoustic metamaterials. After this double negative parameters (negative bulk modulus eff and negative density eff) were produced by this type of medium. Then a group of researchers presented the design and tested results of an ultrasonic metamaterial lens for focusing 60 kHz.

The earlier studies of acoustics in technology, which is called acoustical engineering, are typically concerned with how to reduce unwanted sounds, noise control, how to make useful sounds for the medical diagnosis,sonar, and sound reproduction and how to measure some other physical properties using sound.

Using acoustic metamaterials, the directions of sound through the medium can be controlled ,refraction index, so the traditional acoustic technologies extend to controlling the sound wave and even cloak certain matters from acoustic detection.

Basic Principle

Since the acoustic metamaterials are one of the branch of the metamaterials, the basic principle of the acoustic metamaterials is similar to the pricinple of metamaterials. These metamaterials usually gain their properties from structure rather than composition, using the inclusion of small inhomogeneities to enact effective macroscopic behavior. Similar to metamaterials research, investigating materials with Negative index metamaterials, the negative index acoustic metamaterials became the primary research. Negative refractive index of acoustic materials can be achieved to change the bulk modulus and mass density.

Bulk modulus and mass density

Continuum mechanics

Laws

Conservation of mass

Conservation of momentum

Conservation of energy

Entropy inequality

Solid mechanics

Solids Stress Deformation Finite strain theory Infinitesimal strain theory Elasticity Linear elasticity Plasticity Viscoelasticity Hooke’s law Rheology

Fluid mechanics

Fluids Fluid statics

Fluid dynamics Viscosity Newtonian fluids

Non-Newtonian fluids

Surface tension

Scientists

Newton Stokes Navier Cauchy Hooke Bernoulli

This box: view talk edit

Below, the bulk modulus of a substance reflects the substance’s resistance to uniform compression. It is defined in relation to the pressure increase needed to cause a given relative decrease in volume.

The term mass density of a material, is interchangeable with density. The latter is defined as mass per unit volume and is expressed in grams per cubic centimeter (g/cm3). In all three classic states of matter gas, liquid, or solid the density varies with a change in temperature or pressure, and gases are the most susceptible to those changes. The spectrum of densities is wide ranging: from 1015 g/cm3 for neutron stars, 1.00 g/cm3 for water to 1.2103 g/cm3 for air. Also relevant here are area density which is mass over a (two-dimensional) area, linear density – mass over a one-dimensional line, and relative density, which is a density divided by the density of a reference material, such as water.

For acoustic materials and acoustic metamaterials, both bulk modulus and density are component parameters, which define their refractive index.

Acoustic metamaterial analogues

Bulk modulus – illustration of uniform compression

Scientific research revealed that acoustic metamaterials have analogues to electromagnetic metamaterials when exhibiting the following characteristics:

In certain frequency bands, the effective mass density and bulk modulus may become negative. This results in a negative refractive index. Flat slab focusing, which can result in super resolution, is similar to electromagnetic metamaterials. The double negative parameters are a result of low-frequency resonances. In combination with a well-defined polarization during wave propagation; k = |n|, is an equation for refractive index as sound waves interact with acoustic metamaterials (below):

The inherent parameters of the medium are the mass density , bulk modulus , and chirality k. Chirality, or handedness, determines the polarity of wave propagation (wave vector). Hence within the last equation, Veselago-type solutions (n2 = u*) are possible for wave propagation as the negative or positive state of and determine the forward or backward wave propagation.

In negative refractive, electromagnetic metamaterials, negative permittivity can be found in natural materials. However, negative permeability has to be intentionally created in the artificial transmission medium. Obtaining a negative refractive index with acoustic materials is different. Neither negative nor negative are found in naturally occurring materials; they are derived from the resonant frequencies of an artificially fabricated transmission medium (metamaterial), and such negative values are an anomalous response. Negative or means that at certain frequencies the medium expands when experiencing compression (negative modulus), and accelerates to the left when being pushed to the right (negative density).

Electromagnetic field vs acoustic field

The electromagnetic spectrum extends from below frequencies used for modern radio to gamma radiation at the short-wavelength end, covering wavelengths from thousands of kilometers down to a fraction of the size of an atom. That would be wavelengths from 103 to 1015 kilometers. The long wavelength limit is the size of the universe itself, while it is thought that the short wavelength limit is in the vicinity of the Planck length, although in principle the spectrum is infinite and continuous.

Infrasonic frequencies range from 20 Hz down to 0.001 Hz. Audible frequencies are 20 Hz to 20 kHz. Ultrasonic range is above 20 kHz. Sound requires a medium. Electromagnetics radiation (EM waves) can travel in a vacuum.

Mechanics of lattice waves

An imaginary demonstration: A hypothetical rigid lattice structure (solid) is composed of 1023 atoms. However, in a real solid these particles could just as easily be ions. In a rigid lattice structure, atoms exert pressure, or a force, on each other in order to maintain equilibrium. Atomic forces maintain rigid lattice structure. Most of them, such as the covalent or ionic bonds, are of electric nature. The magnetic force, and the force of gravity are negligible. Because of bonding between atoms, the displacement of one or more atoms from their equilibrium positions will give rise to a set of vibration waves propagating through the lattice. One such wave is shown in the figure to the right. The amplitude of the wave is given by the displacements of the atoms from their equilibrium positions. The wavelength is marked.

There is a minimum possible wavelength, given by the equilibrium separation a between atoms. Any wavelength shorter than this can be mapped onto a wavelength longer than a, due to effects similar to that in aliasing.

Acoustic metamaterials analysis and experiments

The current research on acoustic metamaterials is based not only on prior experience with electromagnetic metamaterials. The key physics in acoustics are sound, ultrasound and infrasound, which are mechanical waves in gases, liquids, and solids. One objective of the inquiry into the properties of acoustic metamaterials is applications in seismic wave reflection and in vibration control technologies related to earthquakes.

Sonic crystals

In the year 2000 the research of Liu et al. paved the way to acoustic metamaterials through sonic crystals. The latter exhibit spectral gaps two orders of magnitude smaller than the wavelength of sound. The spectral gaps prevent the transmission of waves at prescribed frequencies. The frequency can be tuned to desired parameters by varying the size and geometry of the metamaterial.

The fabricated material consisted of a high-density solid lead ball as the core, one centimeter in size, which was coated with a 2.5-mm layer of rubber silicone. These were arranged in a crystal lattice structure of an 8 8 8 cube. The balls were cemented into the cubic structure with an epoxy. Transmission was measured as a function of frequency from 250 to 1600 Hz for effectively a four-layer sonic crystal. A two-centimeter slab absorbed sound that normally would require a much thicker material, at 400 Hz. A drop in amplitude was observed at 400 and 1100 Hz.

The amplitudes of the sound waves entering the surface were compared with the sound waves at the center of the metamaterial structure. The oscillations of the coated spheres absorbed sonic energy, which created the frequency gap; the sound energy is absorbed exponentially as the thickness of the material is increased. The key result here is a negative elastic constant created from resonant frequencies of the material. Its projected applications, with a future expanded frequency range in elastic wave systems, are seismic wave reflection and ultrasonics.

Split-ring resonators for acoustic metamaterials

Copper split-ring resonators and wires mounted on interlocking sheets of fiberglass circuit board. A split-ring resonator consists of an inner square with a split on one side embedded in an outer square with a split on the other side. The split-ring resonators are on the front and right surfaces of the square grid and the single vertical wires are on the back and left surfaces.

In 2004 split-ring resonators (SRR) became the object of acoustic metamaterial research. Prior research with SRRs fabricated as negative index electromagnetic metamaterials was referenced as the progenitor of further research in acoustic metamaterials. An analysis of the frequency band gap characteristics, derived from the inherent limiting properties of artificially created SRRs, paralleled an analysis of sonic crystals. The band gap properties of SSRs were related to sonic crystal band gap properties. Inherent in this inquiry is a description of mechanical properties and problems of continuum mechanics for sonic crystals, as a macroscopically homogeneous substance.

The correlation in bandgap capabilities includes locally resonant elements and elastic moduli which operate in a certain frequency range. Locally resonant elements in electromagnetic metamaterials are microscopic sources embedded throughout the material. In acoustic metamaterials, locally resonant elements would be the interaction of a single 1-cm rubber sphere with the surrounding liquid. The values of the stop band and band gap frequencies can be controlled by choosing the size, types of materials, and the integration of microscopic structures which control the modulation of the frequencies. These materials are then able to shield acoustic signals and attenuate the effects of anti-plane shear waves. By extrapolating these properties to larger scales it could be possible to create seismic wave filters (see Seismic metamaterials).

According to research prior to this analysis, arrayed metamaterials can create filters or polarizers of either electromagnetic or elastic waves. Here a method is shown which can be applied to two-dimensional stop band and bandgap control with either photonic or sonic structures. Similar to photonic and electromagnetic metamaterial fabrication, a sonic metamaterial is embedded with localized sources of mass density and the (elastic) bulk modulus parameters, which are analogous to permittivity and permeability, respectively. The sonic (or phononic) metamaterials are sonic crystals, as in the previous section. These crystals have a solid lead core and a softer, more elastic silicone coating. The sonic crystals had built-in localized resonances due to the coated spheres which resulted in almost flat dispersion[disambiguation needed] curves. Low-frequency bandgaps and localized wave interactions of the coated spheres were analyzed and presented in.

This method can be used to tune bandgaps inherent in the material and, also, create new low-frequency bandgaps. It is also applicable for designing low-frequency phononic crystal waveguides (radio frequency). Doubly periodic square array of SRRs are used to illustrate the methodology.

Phononic crystal

Phononic crystals are synthetic materials that are formed by periodic variation of the acoustic properties of the material (i.e., elasticity and mass). One of the main properties of the phononic crystals is the possibility of having a phononic bandgap. A phononic crystal with phononic bandgap prevents phonons of selected ranges of frequencies from being transmitted through the material.

The basis of phononic crystals dates back to Isaac Newton who imagined that sound waves propagated through air in the same way that an elastic wave would propagate along a lattice of point masses connected by springs with an elastic force constant E. This force constant is identical to the modulus of the material. Of course with phononic crystals of materials with differing modulus the calculations are a little more complicated than this simple model.

Based on Newton observation we can conclude that a key factor for acoustic band-gap engineering is impedance mismatch between periodic elements comprising the crystal and the surrounding medium. When an advancing wave-front meets a material with very high impedance it will tend to increase its phase velocity through that medium. Likewise, when the advancing wave-front meets a low impedance medium it will slow down. We can exploit this concept with periodic (and handcrafted) arrangements of impedance mismatched elements to affect acoustic waves in the crystal essentially band-gap engineering.

The position of the band-gap in frequency space for a phononic crystal is controlled by the size and arrangement of the elements comprising the crystal. The width of the band gap is generally related to the difference in the speed of sound (due to impedance differences) through the materials that comprise the composite.

Double-negative acoustic metamaterial

In-phase waves

Out-of-phase waves

Left: the real part of a plane wave moving from top to bottom. Right: the same wave after a central section underwent a phase shift, for example, by passing through metamaterial inhomogeneities of different thickness than the other parts. (The illustration on the right ignores the effect of diffraction whose effect increases over large distances).

The electromagnetic (isotropic) metamaterials have built-in resonance structures that exhibit effective negative permittivity and negative permeability for some frequency ranges. In contrast, it is difficult to build composite acoustic materials with built-in resonances such that the two effective response functions are negative within the capability or range of the transmission medium.

The mass density and bulk modulus are position dependent. Using the formulation of a plane wave the wave vector is:

The angular frequency is represented by and c is the propagation speed of acoustic signal through the homogeneous medium. With constant density and bulk modulus as constituents of the medium, the refractive index is expressed as n2 = / . In order to develop a propagating (plane) wave through the material, it is necessary for both and to be either positive or negative.

When the negative parameters are achieved, the mathematical result of the Poynting vector . is the opposite direction of the wave vector . This requires negativity in bulk modulus and density. Physically, it means that the medium displays an anomalous response at some frequencies such that it expands upon compression (negative bulk modulus) and moves to the left when being pushed to the right (negative density) at the same time.

Natural materials do not have a negative density or a negative bulk modulus, but, negative values are mathematically possible, and can be demonstrated when dispersing soft rubber in a liquid.

Even for composite materials, the effective bulk modulus and density should be normally bounded by the values of the constituents, i.e., the derivation of lower and upper bounds for the elastic moduli of the medium. Intrinsic is the expectation for positive bulk modulus and positive density. For example, dispersing spherical solid particles in a fluid results in the ratio governed by the specific gravity when interacting with the long acoustic wavelength (sound). Mathematically, it can be easily proven that eff and eff are definitely positive for natural materials. The exception occurs at low resonant frequencies.

As an example, acoustic double negativity is theoretically demonstrated with a composite of soft, silicone rubber spheres suspended in water. In soft rubber, sound travels much slower than through the water. The high velocity contrast of sound speeds between the rubber spheres and the water allows for the transmission of very low monopolar and dipolar frequencies. This is an analogue to analytical solution for the scattering of electromagnetic radiation, or electromagnetic plane wave scattering, by spherical particles – dielectric spheres.

Hence, there is a narrow range of normalized frequency 0.035

This behavior is analogous to low-frequency resonances produced in SRRs (electromagnetic metamaterial). The wires and split rings create intrinsic electric dipolar and magnetic dipolar response. With this artificially constructed acoustic metamaterial of rubber spheres and water, only one structure (instead of two) creates the low-frequency resonances to achieve double negativity.. With monopolar resonance, the spheres expand, which produces a phase shift between the waves passing through rubber and water. This creates the negative response. The dipolar resonance creates a negative response such that the frequency of the center of mass of the spheres is out of phase with the wave vector of the sound wave (acoustic signal). If these negative responses are large enough to compensate the background fluid, one can have both negative effective bulk modulus and negative effective density.

Both the mass density and the reciprocal of the bulk modulus are decreasing in magnitude fast enough so that the group velocity becomes negative (double negativity). This gives rise to the desired results of negative refraction. The double negativity is a consequence of resonance and the resulting negative refraction properties.

Metamaterial with simultaneously negative bulk modulus and mass density

In August 2007 a metamaterial was reported which simultaneously possesses a negative bulk modulus and mass density. This metamaterial is a zinc blende structure consisting of one fcc array of bubble-contained-water spheres (BWSs) and another relatively shifted fcc array of rubber-coated-gold spheres (RGSs) in special epoxy.

Negative bulk modulus is achieved through monopolar resonances of the BWS series. Negative mass density is achieved with dipolar resonances of the gold sphere series. Rather than rubber spheres in liquid, this is a solid based material. This is also as yet a realization of simultaneously negative bulk modulus and mass density in a solid based material, which is an important distinction.

Further information: Poisson’s ratio

Double C resonators

Double C resonator (DCR) is a ring cut in halves. In 2007, proposals have been made for arrays of DCRs and similar negative acoustic metamaterial. Although linear elasticity is mentioned, the problem is defined around shear waves directed at angles to the plane of the cylinders. The DCR was constructed similar to the SRRs in a multiple cell configuration. The DCR has been improved with stiffer material sheets. Each cell consists of a large rigid disk and two thin ligaments. The DCR cell is a tiny oscillator connected by springs. One spring of the oscillator connects to the mass and is anchored by the other spring. The LC resonator has specified capacitance and inductance. The limitations are expressed with appropriate mathematical equations. In addition to the intended limitations is that the speed of sound in the matrix is expressed as c = / with a matrix of density and shear modulus . The resonant frequency is then expressed as 1/(LC).

A phononic bandgap occurs in association with the resonance of the split cylinder ring. There is a phononic band gap within a range of normalized frequencies. This is when the inclusion moves as a rigid body.

The DCR design produced a suitable band with negative slope in a range of frequencies. This band was obtained by hybridizing the modes of a DCR with the modes of thin stiff bars. Calculations have shown that at these frequencies:

a beam of sound negatively refracts across a slab of such a medium,

the phase vector in the medium possesses real and imaginary parts with opposite signs,

the medium is well impedance-matched with the surrounding medium,

a flat slab of the metamaterial can image a source across the slab like a Veselago lens,

the image formed by the flat slab has considerable sub-wavelength image resolution, and

a double corner of the metamaterial can act as an open resonator for sound.

Acoustic metamaterial superlens

In May 2009 Shu Zhang et al. presented the design and test results of an ultrasonic metamaterial lens for focusing 60 kHz (~2 cm wavelength) sound waves under water. The lens is made of sub-wavelength elements and is therefore potentially more compact than phononic lenses that operate in the same frequency range.

High-resolution acoustic imaging techniques are the essential tools for nondestructive testing and medical screening. However, the spatial resolution of the conventional acoustic imaging methods is restricted by the incident wavelength of ultrasound. This is due to the quickly fading evanescent fields which carry the sub-wavelength features of objects.

The lens consists of a network of fluid-filled cavities called Helmholtz resonators that oscillate at certain sonic frequencies. Similar to a network of inductors and capacitors in electromagnetic metamaterial, the arrangement of Helmholtz cavities designed by Zhang et al. have a negative dynamic modulus for ultrasound waves. Zhang et al. did focus a point source of 60.5 kHz sound to a spot size that is roughly the width of half a wavelength and their design may allow to push the spatial resolution even further. This result is in excellent agreement with the numerical simulation by transmission line model, which derived the effective mass density and compressibility. This metamaterial lens also displays variable focal length at different frequencies.

Acoustic diode

An acoustic diode was introduced in August 2009. An electrical diode allows current to flow in only one direction in a wire; it is an essential electronic device which had no analogues for sound waves. However, the reported design partially fills this role by converting sound to a new frequency and blocking any backwards flow of the original frequency. In practice, it could give designers new flexibility in making ultrasonic sources like those used in medical imaging. The proposed structure combines two components: The first is a sheet of nonlinear acoustic materialne whose sound speed varies with air pressure. An example of such a material is a collection of grains or beads, which becomes stiffer as it is squeezed. The second component is a filter that allows the doubled frequency to pass through but reflects the original.