Fundamentals of Ocean Acoustics

Abstract

The origin of computational and numericalacoustics coincides with the emergence of theoretical physics [1] as an intellectual endeavor. Pythagoras developed the theory of the (Western) musical scale in terms of a device called a monochord in which adjacent consonant notes of the musical scale were obtained by plucking two string segments whose relative lengths were ratios of the small integers 1, 2, and 3. He recognized that the lengths of these strings were inversely proportional to the frequency of sound generated when plucked. Since that time, computational methods in acoustics have expanded to use more numbers than these first three integers. Mersenne [2] in the seventeenth century added the irrationals as a numerical tool when he determined that the frequency of a vibrating string was proportional to the square root of its cross-sectional area. He further added to the quantitative tradition of acoustics with conclusions such as: “The velocity of sound is greater than the velocity of cannon balls and equals 230 six-foot intervals per second.” Although the former statement is also probably true for sound propagating in water, Mersenne’s contributions to the understanding of underwater acoustics are suspect judging from his speculation that sound travels more slowly in water than air because the density of water is greater than air.