# Relationship between standing waves and resonance of fate

### Wave - Wikipedia

The modes of vibration associated with resonance in extended objects like strings and air columns have characteristic patterns called standing waves. This produces standing waves, and only certain patterns and frequencies of Resonance phenomena occur with all types of vibrations or waves: there is . links the amplitude of the oscillator to the driving force in frequency space:[12] .. Resonance of Fate[a] is a role-playing video game developed by tri-Ace and. a standing modulated wave forms for driving frequencies below the However, the relation between the phenomena observed . holds in the resonance regions .. Let us also briefly comment on the fate of the two typical.

A two-dimensional standing wave on a disk ; this is the fundamental mode. A standing wave on a disk with two nodal lines crossing at the center; this is an overtone. Light beam exhibiting reflection, refraction, transmission and dispersion when encountering a prism Waves exhibit common behaviors under a number of standard situations, e. Transmission and media[ edit ] Waves normally move in a straight line i.

Such media can be classified into one or more of the following categories: A bounded medium if it is finite in extent, otherwise an unbounded medium A linear medium if the amplitudes of different waves at any particular point in the medium can be added A uniform medium or homogeneous medium if its physical properties are unchanged at different locations in space An anisotropic medium if one or more of its physical properties differ in one or more directions An isotropic medium if its physical properties are the same in all directions Main articles: Absorption acoustics and Absorption electromagnetic radiation Absorption of waves means, if a kind of wave strikes a matter, it will be absorbed by the matter.

When a wave with that same natural frequency impinges upon an atom, then the electrons of that atom will be set into vibrational motion. If a wave of a given frequency strikes a material with electrons having the same vibrational frequencies, then those electrons will absorb the energy of the wave and transform it into vibrational motion.

Reflection physics When a wave strikes a reflective surface, it changes direction, such that the angle made by the incident wave and line normal to the surface equals the angle made by the reflected wave and the same normal line. Refraction Sinusoidal traveling plane wave entering a region of lower wave velocity at an angle, illustrating the decrease in wavelength and change of direction refraction that results.

Refraction is the phenomenon of a wave changing its speed. Mathematically, this means that the size of the phase velocity changes. Typically, refraction occurs when a wave passes from one medium into another. The amount by which a wave is refracted by a material is given by the refractive index of the material. The directions of incidence and refraction are related to the refractive indices of the two materials by Snell's law. Diffraction A wave exhibits diffraction when it encounters an obstacle that bends the wave or when it spreads after emerging from an opening.

Diffraction effects are more pronounced when the size of the obstacle or opening is comparable to the wavelength of the wave. To make the third possible standing wave, divide the length into thirds by adding another node. This gives us one and a half wavelengths.

### Standing waves and resonance

It should become obvious that to continue all that is needed is to keep adding nodes, dividing the medium into fourths, then fifths, sixths, etc. There are important relations among the harmonics themselves in this sequence. Since frequency is inversely proportional to wavelength, the frequencies are also related.

The simplest standing wave that can form under these circumstances has one node in the middle. To make the next possible standing wave, place another antinode in the center. To make the third possible standing wave, divide the length into thirds by adding another antinode. It should become obvious that we will get the same relationships for the standing waves formed between two free ends that we have for two fixed ends. The only difference is that the nodes have been replaced with antinodes and vice versa.

Thus when standing waves form in a linear medium that has two free ends a whole number of half wavelengths fit inside the medium and the overtones are whole number multiples of the fundamental frequency one dimension: A node will always form at the fixed end while an antinode will always form at the free end. The simplest standing wave that can form under these circumstances is one-quarter wavelength long. To make the next possible standing wave add both a node and an antinode, dividing the drawing up into thirds.

## Standing waves and resonance

We now have three-quarters of a wavelength. Repeating this procedure we get five-quarters of a wavelength, then seven-quarters, etc. In this arrangement, there are always an odd number of quarter wavelengths present.

Thus the wavelengths of the harmonics are always fractional multiples of the fundamental wavelength with an odd number in the denominator. Likewise, the frequencies of the harmonics are always odd multiples of the fundamental frequency. The three cases above show that, although not all frequencies will result in standing waves, a simple, one-dimensional system possesses an infinite number of natural frequencies that will. It also shows that these frequencies are simple multiples of some fundamental frequency.

For any real-world system, however, the higher frequency standing waves are difficult if not impossible to produce. Tuning forks, for example, vibrate strongly at the fundamental frequency, very little at the second harmonic, and effectively not at all at the higher harmonics.

It seems like getting something for nothing. Put a little bit of energy in at the right rate and watch it accumulate into something with a lot of energy. This ability to amplify a wave of one particular frequency over those of any other frequency has numerous applications. Basically, all non-digital musical instruments work directly on this principle.

What gets put into a musical instrument is vibrations or waves covering a spread of frequencies for brass, it's the buzzing of the lips; for reeds, it's the raucous squawk of the reed; for percussion, it's the relatively indiscriminate pounding; for strings, it's plucking or scraping; for flutes and organ pipes, it's blowing induced turbulence.

## Standing Waves

What gets amplified is the fundamental frequency plus its multiples. These frequencies are louder than the rest and are heard. All the other frequencies keep their original amplitudes while some are even de-amplified. These other frequencies are quieter in comparison and are not heard. You don't need a musical instrument to illustrate this principle. Cup your hands together loosely and hold them next to your ear forming a little chamber.

You will notice that one frequency gets amplified out of the background noise in the space around you. Vary the size and shape of this chamber. The amplified pitch changes in response. This is what people hear when the hold a seashell up to their ears. It's not "the ocean" but a few select frequencies amplified out of the noise that always surrounds us. During speech, human vocal cords tend to vibrate within a much smaller range that they would while singing.

How is it then possible to distinguish the sound of one vowel from another? English is not a tonal language unlike Chinese and many African languages. There is little difference in the fundamental frequency of the vocal cords for English speakers during a declarative sentence.

Interrogative sentences rise in pitch near the end. Vocal cords don't vibrate with just one frequency, but with all the harmonic frequencies. Different arrangements of the parts of the mouth teeth, lips, front and back of tongue, etc. This amplifies some of the frequencies and de-amplifies others.

The filtering effect of resonance is not always useful or beneficial. People that work around machinery are exposed to a variety of frequencies. This is what noise is. Everyone should know that loud sounds can damage one's hearing.

What everyone may not know is that exposure to loud sounds of just one frequency will damage one's hearing at that frequency.