Near and far field

In the propagation of a sound wave to be distinguished from the signal source with very different physical properties, with the near field and the far field two distance ranges.

The near field refers to the immediate area around the sound source, which is characterized by a non-uniform alternating between hot and constructive and destructive interference. In contrast, the far-field refers to a region which is far away from the sound source. Interference effects play only a minor role for the structure of the sound field here. In particular, in a fluid medium in the far field pressure and velocity are in phase, so that the fluid is a real-valued wave impedance can be defined. The distance at which the near field passes into the far field, is dependent on the acoustic wavelength and the size of the transducer. Is used to distinguish between near and far field alone the direct sound generated by the sound source, that is considered the radiation characteristics of the transducer and the properties of the propagation medium. Near-field and far-field are not space dependent, but sound- source-dependent. Reflections from objects in space such as the diffuse field generated by the walls or standing waves go into the consideration not to.

Monopole radiator

The boundary between the near and far field is rendered as a breathing sphere ( or pulsating sphere) with radiation in the room at the example of a radiator of zero order. The wave equation for a spherical wave provides for the sound pressure, the solution:

For the sound velocity applies:

For the acoustic impedance

In this case, mean

  • P0 = pressure amplitude
  • K = angular wave number
  • R = distance of the measurement point from the spherical radiator
  • Z0 = characteristic acoustic impedance
  • I is the imaginary unit with the property

Far-field

The far-field is characterized by the condition

Thereby reducing the formula to be simplified for the sound velocity

In the far field so there are between sound pressure and particle velocity no phase difference, which is evident when considering the ( measurable ) indicates Real shares of Euler's formula for both sound field quantities:

Near field

The near field is characterized by the condition

Thereby reducing the formula to be simplified for the sound velocity

In the near field, therefore, sound pressure and particle velocity differ in two major ways:

  • The sound velocity decreases quadratically with increasing distance and
  • Between and there is a phase difference of 90 °, which can be seen when one sound field sizes for both specifying the ( measurable ) real components of Euler's formula:

The sound pressure of the sound particle velocity approaches a maximum advance of 90 °. At the transmitter site ( in the immediate near field of the ball transmitter ) only reactive power occurs and the acoustic impedance is ( almost) purely imaginary. This means that the monopole radiator emits energy at certain time interval to the environment and then almost exactly the same amount of energy absorbed again ( it "breathes "). The small difference is radiated in the far field and is measurable.

Transition region

The transition between near and far field is continuous. Defining characteristic is the rest phase angle between sound pressure and particle velocity. This varies continuously between 90 ° in the immediate vicinity of the monopole radiator to 0 ° at a distance of many wavelengths. The boundary is often pulled at r ≈ λ because the clamp in the formula for the sound velocity then the value

Has.

Extended spotlight

In the acoustic dipole radiators are used as in the high-frequency technology rarely whose dimensions correspond approximately to the wavelength. One reason for this is the dimension of the transducer handle at audio frequencies, the emission of a very wide frequency spectrum, wherein ultrasound. The following example shows the harmonic through simulations, sound field of a 4 MHz unfocused ultrasound transducer to the transducer diameter D = 10 mm in water with a speed of sound. The sound field specified solves the boundary value problem for the emission of a sound- hard boundary surface z = 0 in the half-space. The radiation can be described by a uniform coating of the active transducer surface with monopole sources.

The transition from the near field to the far-field occurs at the furthest from the surge transducer remote sound pressure maximum on the acoustic axis. The distance between the ultrasonic transducer and the last sound pressure maximum on the acoustic axis is as so-called near-field

Referred to. It is in the example.

The figure shows pronounced interference structures with an irregular alternating between locations constructive and destructive interference in the near field. The far field has a regular structure with a steady drop in sound pressure with distance from the transducer.

Distinction between

The acoustic near field and far-field terms are not always clearly distinguish the expressions of direct field or free field and diffuse field. Near and far field identify the sound source itself, while the direct field (free field) and diffuse field are determined by the room acoustic properties of the surrounding space.

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