# Fashions

The first six modes of a resonator

A Mode (of English. Mode ), also vibration mode in which acoustic even spatial mode , in mechanics also eigenmode , natural oscillation mode or partial oscillation is in the physics , the description of certain time-stationary properties of a shaft . The wave is described as the sum of different modes.

The modes differ in the spatial distribution of the intensity . The shape of the modes is determined by the boundary conditions under which the wave propagates. In contrast to the thematically related normal vibrations, the analysis of vibration modes can be applied to both standing and continuous waves.

## In acoustics

### Room fashions

Room modes can be used to characterize the room acoustics of a concert hall .

The room modes discolour the sound of a room because certain tones are particularly prominent and have an uneven distribution of energy within the room. If discrete resonance frequencies occur, these are more noticeable than if many resonance frequencies are evenly distributed in the spectrum ( reverberation ).

A standing wave. As you can see here, at the ends (the room delimitation) a pressure belly appears as a maximum.

A certain resonance frequency distribution is a physical property of the room that depends on its dimensions. Only certain frequencies are excited. Both the increased level and the duration of the tone play a role in these resonance effects .

Room fashions between two hard walls. There must always be maximum sound pressure on the walls , which can be seen from the pressure bulges.

Above about 300 Hz ( Schröder frequency ), acoustic modes of the room in living rooms do not cause any audible distortion of the reproduction because the modes merge into one another in the form of dense reflections and reverberation . Below 300 Hz, however, they can cause perceptible discoloration of the sound. Since these affect the particularly low tones, this is perceived as droning , booming or one-note bass . The amplitude of an acoustic mode depends on its position in space. The degree of discoloration therefore differs from place to place.

There are three types of standing modes in the acoustics of a typical ( cuboid ) listening room:

• axial (longitudinal) modes that clearly dominate
• tangential and
• diagonal modes (also called obligue or oblique modes).

Their frequencies can be calculated as follows:

${\ displaystyle f _ {\ mathrm {n_ {x} / n_ {y} / n_ {z}}} = {\ frac {c_ {S}} {2}} {\ sqrt {\ left ({\ frac {n_ {x}} {L}} \ right) ^ {2} + \ left ({\ frac {n_ {y}} {B}} \ right) ^ {2} + \ left ({\ frac {n_ {z }} {H}} \ right) ^ {2}}} \,}$

Where:

• ${\ displaystyle f}$the frequency of the mode in Hz
• ${\ displaystyle n_ {x}}$ the order of fashion room length
• ${\ displaystyle n_ {y}}$ the order of the fashion room width
• ${\ displaystyle n_ {z}}$ the order of fashion room height
• ${\ displaystyle c_ {S}}$ the speed of sound 343 m / s at 20 ° C
• ${\ displaystyle L}$, , The length, width and height of the room in meters.${\ displaystyle B}$${\ displaystyle H}$

### More acoustic fashions

The flexural oscillator clamped on one side - the deflection amplitude of the second mode is shown

In acoustics, the modes determine the relative strength of the overtones and thus the sound of an instrument , e.g. B. an organ pipe or a bell .

#### Flexural oscillator

Bars clamped on one side are called flexural oscillators . These can vibrate in several modes.

#### Membrane vibrations

Mode (1s)${\ displaystyle u_ {01}}$
Fashion (5d)${\ displaystyle u_ {23}}$
Vibration pattern of a clamped, rectangular plate

A clamped, thin surface ( membrane ) like a drum can show many different vibration modes. These partial oscillations lead to irregularities in the frequency response of loudspeakers .

#### Cavities

Acoustic cavity resonators are e.g. B. the Helmholtz resonator or Kundt's tube , but they also play a major role in loudspeaker boxes ( bass reflex box ) and wind instruments and organ pipes .

#### Solid

Different acoustic vibration modes in solids occur, for example, in quartz crystals , bells , gongs , chime bars , triangles , etc. In addition to the basic resonance frequency, all these bodies can also be excited in higher oscillation modes or, due to the different composition of their oscillation modes, have a certain sound character. In solids, due to the existing shear modulus , transverse wave and oscillation modes can also occur.

The shape of housings and machine parts determines which vibration modes are particularly excited during operation. With a suitable, rather irregular shape, the formation of oscillation modes based on shape symmetries can be avoided; Sound radiation and fatigue due to vibrations can thus be reduced.

## Electromagnetic waves

For electromagnetic waves such as light , laser and radio waves , the following types of modes are distinguished:

• TEM or t ransversal- e lektro m agnetic Mode: Both the electrical and the magnetic field component are always perpendicular to the propagation direction. This fashion is only capable of spreading if either
• TE or H modes: Only the electric field component is perpendicular to the direction of propagation, while the magnetic field component points in the direction of propagation.
• TM or E modes: Only the magnetic field component is perpendicular to the direction of propagation, while the electric field component points in the direction of propagation.

The last two modes are particularly important in waveguides .

TEM waves are not restricted in their frequency, which means that they can propagate over the entire frequency spectrum. TM and TE waves, on the other hand, can only propagate above a certain frequency ( cutoff frequency ) that is dependent on the geometry of the conductor . As a result, several modes can be capable of propagation at the same time at a fixed frequency. However , this state is undesirable in data transmission , since signal integrity, that is , low- dispersion operation of waveguides, can only be guaranteed with mode purity. Waveguides (e.g. cables or waveguides ) can therefore only be used sensibly for signal transmission up to the cutoff frequency of the first higher mode.

In laser technology , modes are an important tool for characterizing a laser beam. In particular, the transverse modes are of interest here, which differ in the distribution of the intensity perpendicular to the direction of propagation. See also mode volume .

In electrical engineering, for some devices to function optimally it is necessary that a wave mainly contains a certain mode. Examples of this are the magnetron of a microwave oven or the crystal of an oscillating quartz .

In the case of antennas, on the other hand, it is often desirable that no mode is strongly preferred.