492 VIGOUREUX AND HEBSEY [CHAP. 12 



In cases when measurements are required at one frequency only, for example 

 for determination of transmission loss at a sonar frequency, the untuned 

 detector is not necessarily the best instrument ; a sonar transducer identical 

 with the one used for transmission has the advantage of sensitivity and free- 

 dom from interference by sound of other frequencies. 



B. Frequency Analysis 



The spectrum is an important characteristic of a signal. Spectra may be 

 continuous, like those of water noise, animal noise or cavitation, or they may 

 be discrete ; singing propellers and vibrations transmitted by machinery are 

 examples of discrete or "line" spectra; these spectra are specified by decibels 

 referred to an arbitrary intensity or pressure at the conventional distance of 

 1 yard, whereas continuous spectra are specified in terms of spectrum level, i.e. 

 decibels above an arbitrary intensity or pressure in a band 1 cycle per second 

 wide encompassing the frequency of interest. [Unfortunately a single arbitrary 

 reference is not in general use. Those most often quoted are : 1 watt per square 

 metre (intensity), 1 dyne per square centimetre, and 0.0002 dyne per square 

 centimetre (pressure).] When plotted against frequency they appear as con- 

 tinuous curves without discontinuities whereas discrete spectra consist of lines 

 perpendicular to the frequency axis. 



The untuned detector is normally employed to determine spectral distribu- 

 tion, with at some stage of the amplifier a band-pass filter of known shape, the 

 central frequency of which can be shifted smoothly throughout the range by 

 heterodyning or otherwise. The output, usually rectified, is displayed on a pen 

 recorder or cathode-ray oscillograph ; with a square-law rectifier the deflection 

 is directly proportional to the power in the band. For discrete spectra, the filter 

 must be sufficiently narrow to exclude lines other than the one under measure- 

 ment whereas, for continuous spectra, a wider band may be preferable in order 

 to render amplifier noise unimportant. 



In the case of sustained noise or of signals of long duration, the spectrum 

 measured as explained above is a power spectrum. But it is often desired to 

 know the distribution of energy with frequency in a pulse, as for instance that 

 produced by the explosion of a charge. The same apparatus is suitable provided 

 the time constant of the recorder is small enough to reproduce the rise and fall 

 of the output ; the energy is then proportional to the area under the output 

 curve. Alternatively, the output can be integrated by an electric circuit of time 

 constant much greater than the duration of the signal, when the recorder then 

 reads energy directly. Several analyzers especially designed for the study of 

 pulses and other transient sounds, such as speech, have been developed during 

 the past twenty years. One in particular reported by Koenig, Dunn and Lacy 

 (1946) and further treated by Koenig and Ruppel (1948) has proved most 

 useful in underwater acoustical research. The instrument is described and 

 several examples of its use are recounted in Chapters 13 and 14. 



