RODERICK: FORWARD SCATTERED LOW-FREQUENCY SOUND FROM THE SEA SURFACE 



insonified area, and conditions could be generated that modeled low- 

 frequency sound propagation interacting with the gravity waves of the 

 sea surface. Predictions were made for the normalj.zed pressaie re- 

 flected and scattered from a traveling sinusoidal surface of angular 

 frequency w , wave height h, and wave number k. The wave is propagating 

 in a direction that makes an angle a with a vertical plan containing 

 the angle of incidence and reflection. 



An interesting result is observed for the scattered sound: the 

 spectrum of the reradiation contains upper and lower sidebands posi- 

 tioned symmetrically about the transmitted frequency co and displaced 

 from to by multiples of the surface frequency. The amplitudes of the 

 frequency components are given by Bessel functions of the first kind 

 and of order n. The argument of the Bessel functions are dependent 

 on the angles of incidence and scatter, wave height, and acoustic wave 

 number. These relationships are summarized in the following equation: 



+00 



p = >, F (e,,e^,e ) j (c kh) 



^— ' n 1 2 3 n n 



exp .j -i (00 - nu)^) t - ^ + (^^ j l (5) 



When the surface wave length is much larger than the acoustic 

 wave length, most of the acoustic energy is scattered close to the 

 specular direction, and it is not possible to resolve the specularly 

 scattered signal (see Figure 3) . The acoustic energy is scattered 

 in space in selected directions determined by the familiar diffraction- 

 grating equation of order n. (This same equation appeared in Flatte's 

 talk (these Proceedings) during the discussion of the interaction of 

 internal waves and acoustic fields.) The carrier frequency is 



332 



