Extraneous Frequencies Generated in Air Carrying Intense Sound Waves

ECENT developments in horn type loud speakers1 for high quality reproduction of intense sounds necessitate a consideration of the more exact equations of wave motion if distortion due to the generation of extraneous frequencies in the air of the horn itself is to be avoided. Similar considerations may be of some importance in connection with the pick-up of intense sounds. The propagation of waves of finite displacement has interested physicists for more than a century. In 1808 Poisson derived an equation which shows that, in general, a sound wave cannot be propagated without a change in form and consequent generation of additional frequencies. This distortion is caused by the non-linearity of air; that is, if equal positive and negative increments of pressure are impressed on a mass of air the changes in volume of the mass will not be equal; the volume change for the positive pressure will be less than the volume change for the equal negative pressure. An idea of the nature of the distortion can be obtained from the adiabatic curve AB for air as given in the familiar volume pressure indicator diagram (Fig. la). The undisturbed pressure and specific volume of air are indicated by point P0 V0 . Any deviation from the tangent through this point causes distortion and consequent generation of extraneous frequencies. The theoretical magnitudes of the waves of extraneous frequencies are obtained from a solution of the exact differential equation of wave propagation in air. The solution shows that the pressure of the second harmonic frequency, which is generated in the air, increases with the frequency and the magnitude of the fundamental * Published in the January 1935 issue of the Jour.