330 



VARIABILITY AND FREQUENCY CHARACTERISTICS 



the rapid frequency shifts characteristic of reverbera- 

 tion. This device " measures the time interval be- 

 tween successive zeros of the alternating signal fed 

 into it. The "instantaneous frequency" of the signal 

 is interpreted as inversely proportional to the meas- 

 ured time interval between successive zeros. This 

 instantaneous frequency is recorded against time on 

 a cathode-ray oscilloscope (which may be photo- 

 graphed); the frequency appears as a spot whose 

 deflection from a base line is a measure of the 

 frequency. 



The periodmeter is designed to function in the 

 neighborhood of 800 c; thus reverberation must be 

 heterodyned to about this frequency before frequency 



Figure 4. Periodmeter record of 800-cycle oscillator 

 tone. 



analysis by the periodmeter is possible. Figure 4 is 

 the photograph of a trace obtained by feeding an 

 800-c oscillator tone into the periodmeter. Figure 5 

 shows the traces of a ping and its echo from an S-class 

 submarine; the way the echo mirrors the frequency 

 fluctuations in the ping is interesting. Figures 6A and 

 6B are observed traces for volume reverberation and 

 bottom reverberation, both showing no indication of 

 a definite law for the variation of reverberation fre- 

 quency with time after midsignal. Such traces are 

 typical of most reverberation. In all these traces, in- 

 crease in frequency is indicated by a smaller (lower) 

 amplitude on the trace. 



The periodmeter has been used to analyze rever- 

 beration signals. The results of this analysis will be 

 first summarized and then discussed in more detail. 

 Since all these conclusions are based on more than 

 1,000 observed points, they have a high degree of 

 statistical probability. 



1. There are no obvious systematic changes in 

 spectral character during the decay of a single rever- 

 beration. If the average pitch does change with time 

 after midsignal in any systematic way, such a trend 

 is masked by the much larger irregular variations in 

 pitch. 



2. The averages of reverberation frequency over 

 time intervals corresponding to the pitch response 

 time of the ear (0.1 sec) show variations large enough 

 to render target doppler discrimination of 1 knot or 

 less highly unreliable. For target speeds of 2 knots 

 or more, target doppler discrimination appears quite 

 reliable. 



3. If the outgoing signals are unintentionally fre- 

 quency-modulated, because of poor design or malad- 

 justment of the transmitting equipment, the rms fre- 

 quency spread in the reverberation is increased. 



4. The frequency spread of the heterodjmed rever- 

 beration depends on the audio output frequency and 

 the pulse length. The rms frequency spread A/ was 

 well-fitted by the formula 



Af = Kf^' r-'^ (9) 



where / is the audio output frequency, r is the pulse 

 length, and K is a constant. Pulses of length 92 msec 

 and frequency 24 kc produced reverberation, which, 

 after being heterodyned to 800 c, had a mean rms 

 frequency spread of 21.5 c. 



5. The frequency spread of reverberation does not 

 seem to depend on the frequency of the outgoing 

 signal. 



6. The mean observed reverberation frequency 

 agreed with own-doppler values calculated for the 

 axis of the projector. At moderate ship speeds, the 

 finite width of the projector beam did not, through 

 own-doppler effects, cause marked broadening of the 

 beam. 



Most of the above results are quite reasonable. 

 The first result indicates that the reverberation arises 

 from a process which is essentially random. The 

 last result indicates that the mean reverberation 

 frequency can be used as a reference for the measure- 

 ment of target doppler. That is, the mean reverbera- 

 tion frequency /i agrees with the following formula 

 for the frequency of an echo received on a moving 

 ship from a stationary target. 



/i =/(^l+^cos9J, 



(10) 



where v is the velocity of the echo-ranging ship, 6 is 

 the angle between the projector axis and the line of 

 motion of the ship, / is the frequency of the emitted 

 ping, and c is the velocity of sound. This agreement 

 is theoretically expected.'^- '' 



The second result indicates that estimates of target 

 doppler are not reliable unless the target is moving at 

 speeds of 2 knots or more. The third result, that the 



