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# Fundamentals of Acoustics: Sound Fields

By Marshall Williams 28 January 2021

There are a range of terms describing acoustic fields to be familiar with when working in acoustic applications. The common ones that you will come across are:

• Free Field
• Diffuse Field
• Near Field
• Far Field

## Free Field & Diffuse Field

A free field is a region where the acoustic waves can propagate free from obstructions that would otherwise interfere with the sound path.

For transducer simulations, free field conditions are typically used to characterize fundamental device performance.

A diffuse field is essentially the opposite of a free field. Diffusion, with regards to sound, is the scattering or reflections of sounds waves. A diffuse field is therefore constructed of reflected waves and has a unique property of uniform pressure in the field.

A reverberant chamber is commonly used to generate diffuse fields to characterize acoustic materials.

## Near Field & Far Field

When an acoustic source is emitting acoustic waves to generate a sound field, it can be separated into two distinctive zones: the near field and far field.

The near field as the name suggests, is the region of space close to the emitting source. In this region, there is typically a complex constructive and destructive interference pattern due to the waves being generated from an aperture of a set geometric size.

The animation shows a 5 cycle sinusoidal pulse emitting from a source (left) and the resultant maximum pressure field (right) to highlight the variation in pressure levels in the near field:

This region of interference in the near field can be determined using the following equation:

Near Field Length= d2f ⁄ 4.v = d2  ⁄ 4.λ

Equation 1: Near field calculation for a circular aperture [1]

Where:

• d is the diameter of the circular aperture
• f is the frequency of operation
• v is the velocity of the acoustic media
• λ is the wavelength in the acoustic media

The equation above can be modified slightly for square/rectangular apertures by substituting the diameter for a length (l) and using an aspect ratio constant (k):

Near Field Length = k.l2 f ⁄ 4.v = k.l2 ⁄ 4.λ

Equation 2: Near field formula for a square/rectangular aperture [2]

Once the interference pattern of the near field ends, the far field begins. This point is also considered the natural focus of the device.

In the far field region, the source can be treated as a point source. The wave front is deemed as a plane-wave and will decay at rate of 6 dB per distance doubled from the source.

Most transducers are characterized and operate in the far-field as behavior is consistent across a range of frequencies required by specific imaging applications in sonar, non-destructive testing or biomedical industries.

We hope you have enjoyed our fundamentals of acoustics mini blog series. Why not take what you have learned and try simulating acoustics in OnScale! Check out the tutorials on our Help Center to help you get started.

References:

[1] Ultrasonic Inspection – Near Field Calculation (https://www.nde-ed.org/GeneralResources/Formula/UTFormula/near_field/near.htm)

[2] A Review of Conventional Beam Characteristics (https://www.olympus-ims.com/en/ndt-tutorials/transducers/characteristics/)