1 knot; this Doppler effect must be taken into account. Since only a 

 comparison of wave spectra is desired, in this case, it is only necessary 

 to impose the same experimental conditions on the two systems. This was 

 accomplished by a frequency transformation on the SPLASHNIK wave spectrum 

 for a speed of 4 . 5 knots into the waves. The transformation is given by 



= OD + Oi 



where the Jacobian 



2 V 



cos X [5] 



T _ — 



^ = ^ [6] 



is incorporated to conserve the energy in the transformed spectrum. 



The transformation of the spectrum given by Equations [5] and [6] 

 results in an estimate of the spectrum which would have been measured if 

 the SPLASHNIK had traveled into the waves (X = 0) at a speed (v) of 4.5 

 knots. Of course, the drift of the SPLASHNIK is a guess and the trans- 

 formation assumes that the waves were all traveling in one direction; never- 

 theless at low speeds, the estimate should be fairly reliable. Figure 8b 

 shows the computed and transformed SPLASHNIK wave spectra, and Figure 8c 

 shows the shipborne wave recorder (SBWR) spectrum superimposed on the 

 transformed SPLASHNIK spectrum. The SPLASHNIK peak is somewhat lower than 

 the SBWR peak and is located at a slightly higher frequency, but shows 

 more energy at higher frequencies than the shipborne wave recorder. In 

 any case, the two speccra have the same general form and the rms wave 

 heights as shown in Figure 8c are fairly close. A second case (Figure 9), 

 shows even better agreement in spectral shape and a remarkable agreement 

 in rms wave height . 



It has been noted that the SPLASHNIK drifts. It is, of course, 

 desirable to measure the waves at a fixed point and consequently a trans- 

 formation is suggested to account for the drift. In view of Figure 8b, 



13 



