Underwater Acoustics

The directivity index DI is a measure of the directionality of projectors and hydrophones. For a projector this specifies the distribution of acoustic energy. The significance for a hydrophone lies in its ability to discriminate against an omnidirectional noise level NL when listening to a signal from a specific direction.

The effect is to improve the signal to noise ratio, SNR, which can then be given as:

The Dl can also be considered as a simple form of array gain, rather than a means of noise reduction. The effect is the same.

Whilst the DI has no reference level, due to the underlying directivity ratio being unitless, the "signal to noise ratio", somewhat confusingly does have units of time.

This can be seen by noting that a noise level NL must have a defined bandwidth. For the simple case of uniformly distributed "white noise", the energy is proportional to the bandwidth, so can be given in Watts/Hz. More usually it is given as a pressure spectrum level, where the notional bandwidth is 1 Hz, so that the units are Pa²/Hz. The spectral distribution can then be plotted against frequency.

In contrast, the energy of a narrow band tonal signal is represented by the mean square pressure in Pa², irrespective of the measurement bandwidth (providing the tonal frequency lies within this band).

Now the SNR has units of time (seconds). This helps to explain why SNR values quoted without reference to the bandwidth of the measurement system are highly misleading or even meaningless.

Artificial sonar systems may vary the receiver bandwidth to optimise performance. Whilst a narrow band will reject noise better, a wider band will give a faster response to give more precise timing or to allow the use of complex codes. Natural sonar systems used by marine mammals and other creatures will also have an effective bandwidth (masking bandwidth or critical bandwidth). It is important that this is considered when assessing the effects of noise on the hunting performance of creatures which depend on their sonar systems.

Human hearing in air has been shown to exhibit masking bandwidths which approximate to 1/3rd octave bands, for which the upper limit frequency exceeds the lower limit by a ratio of ³√2 or 1.256.