Calculation of Second‐Harmonic Generation in a Piston Beam

We discuss the nonlinear generation of a second‐harmonic component in the first‐harmonic beam from a circular plane piston, radiating into a fluid. First‐order perturbation theory is used; higher harmonics, absorption, and depletion of each harmonic are ignored, although a partial correction for the last two effects is applied later. The ratio of piston diameter to first‐harmonic acoustic wavelength is assumed to be about 30 or greater. In particular, the axial behavior of the second harmonic, which has marked structure, is found to agree well with experimental results in water. Also, the average value of the second‐harmonic field is calculated over a circle coaxial with the source, parallel to it, and of the same size. This average differs considerably from the result of an oversimplification that treats the first‐harmonic beam as cylindrically collimated plane waves. When compared with measurements in water, the average agrees well at a source pressure of 3 atm but progressively less well at 5 and at 6 ...