# Responses, Directivity and Intensity

VOLUME 3, OCTOBER 2010

M.Sc. Physics, Instrumentations (UTM Skudai)
B.Sc. Physics, Industrial Physics (UTM Skudai)

Project title:Micromachined Parametric Array Acoustic Transducers for Sonar Application

Principle of Underwater Acoustic Transducer Design (Part 2)

Responses, Directivity and Intensity

Responses for the acoustic transducer measure the ability to perform radiation and detection of sound. In most cases, sound that was radiated into the medium need to be detected by the same transducer module or array. In more technical manner, response can be defined as transducer output per unit input as a function of specific parameters; it can be frequency, fixed drive condition or dimensional parameters.

Directivity of the radiated sound from the transducer changes with frequency of the signal and the distance from the transducer. However, beyond the far field at a fix frequency, directional characteristics of the transducer become independent of distance. At this point, sound intensity is inversely proportional to distance. The direction in which the maximum acoustic intensity occurs is known as the acoustic axis or maximum response axis (MRA).

Another important term from this interpretation is the directivity factor. It can be defined as the ratio of maximum acoustic intensity, Io to the acoustic intensity averaged from all directions, Ia; at the same distance in the far field. For a deeper understanding, average intensity, Ia need to be interpreted as the total radiated acoustic power, W divided by the area of a sphere at the distance, r. Mathematically, directivity factor can be written as:

As a standard practice, directivity index was stated in decibel (dB) of directivity factor which is;

For a conventional macro size transducer, when the area of a vibrating surface of a transducer, A is larger than acoustic wavelength, with the assumption of uniform normal velocity of the surface, the directivity factor can approximately be stated as:

Another vital characteristic of the acoustic transducer is the source level. It can be interpreted as a measure of a far field pressure can be produced by a transducer at its maximum response axis. In a lossless medium, total radiated power is independent of distance. However, since the pressure varies inversely with distance, reference distance for a source level is a must. As a standard measure, it is 1m from the acoustic center of the transducer. The source level is defined as a ratio of rms pressure amplitude 1m from the transducer, to 1 micropascal of reference sound level in decibel (dB) which is:

The source level can also be written in terms of total radiated acoustic power and the directivity index by using those relationships:

where

And p is a density of the medium and c is a speed of sound in the medium (both a constant for every specific medium). As the example, for a water which

With W as the output power in Watt is the input electrical power reduced by the electroacoustic efficiency. Source level that correspond to the maximum acoustic power is a very important measure of the acoustic projector. Furthermore, transmitting voltage and current response are defined as a source level for an input of 1V or 1A rms. However, the free field voltage receiving response is different. It can be defined as the open circuit voltage output for a free field pressure input of 1 uPa in a plane wave arriving on the MRA.

References

[1] C.H. Sherman and J.L. Butler, Transducers and Arrays for Underwater Sound, Springer 2007
[2] L.M. Brekhovskikh and Yu. P. Lysanov, Fundamentals of Ocean Acoustics, AIP Press and Springer, 2003.
[3] R.C. Dorf, The ocean Engineering Handbook, CRC Press LLC, 2001.

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