Page 60 - Fall2019

Nonlinear Acoustics Today
decreases faster than that of an ordinary sound wave due to strong energy dissipation at the shock front.
Supersonic Sources
Pressure waves generated by a moving object deserve separate consideration. At low velocities (much less than the sound speed), sound waves are barely excited because the liquid or gas in which the body moves merely flows around it without experiencing much compression. At higher velocities, the flow over the body begins to be accompanied by compres- sion of the medium just ahead of the body and expansion just behind it. These disturbances become acoustic waves. The most interesting situation is when the speed of the object exceeds the speed of sound (about 343 m/s in air) because another type of wave phenomenon arises, a sonic boom. A supersonic object (typically a plane, but it can be a bullet from a gun or a meteor coming from space) moves through the medium faster than the acoustic waves can propagate away. This results in the waves combining to form a cone (the Mach cone) that follows the supersonic object, much like a boat wake. The ratio of the speed of the object (V) to the speed of sound (c) is defined as the Mach number (M = V/c). A Mach cone is created whenever M > 1, and the angle of the Mach cone becomes smaller as M increases.
Sonic booms currently attract the interest of researchers in connection with the possibility of developing a new genera- tion of supersonic civilian aircraft. A loud bang sweeping across land under the plane can have an undesirable effect on buildings, structures and, of course, people (Figure 5). The impact of the sonic boom depends largely on the size of the aircraft, the distance to the observer, and, to a lesser extent, the shape of the aircraft (Rogers and Magl- ieri, 2015; Loubeau and Page, 2018). Near the aircraft, the sonic boom can have a complex shape with a spatial extent approximately the size as the aircraft; this results in a dura- tion of about 0.1 s for a fighter size aircraft and about 0.5 s for a space shuttle or an airplane such as the Concorde. The duration of the sonic boom increases during propaga- tion because the head (compression) shock is supersonic and the tail (rarefaction) shock is subsonic, and the shocks merge until near the ground where the waveform typically resembles the letter N with a bow shock and stern shock. For longer durations, the sonic boom can be perceived as a double “boom” because the two shocks are sufficiently separated in time to be resolved by the human ear. When the plane is nearby, the N wave is shorter, and the sonic boom sounds like a single sharp bang.
Ultrasonic Heating
Nonlinear acoustic effects extend beyond the waveform distortion and harmonic generation. For example, energy transfer to higher harmonics results in increased attenua- tion because high frequencies are typically absorbed more readily. The loss mechanisms convert wave energy into heat. Consequently, the temperature of the medium increases, an effect that depends nonlinearly on the wave amplitude. In the simplest case of a sinusoidal wave, the heat sources and the resulting temperature increase are proportional to the wave intensity, such as the square of the wave amplitude. If the wave contains shocks then the heat sources are even stronger, proportional to the cube of the pressure jump at the shock front (Sapozhnikov, 2015).
One current application of heating generated by acoustic waves is in medicine, where high-intensity focused ultra- sound (HIFU) is used for remote thermal or mechanical destruction of tumor tissue deep inside the body (Bailey et al., 2003). When strongly nonlinear waves are used, a sinusoidal waveform radiated by the transducer evolves into periodic
Figure 6. The role of shock waves in noninvasive HIFU therapy. Top left: numerical modeling of a pressure waveform at the focus of a 1.2- MHz, 256-element, 14-cm-diameter, 14-cm focal length therapeutic array operating at 800 W acoustic power assuming linear (black curve) and nonlinear (blue curve) propagation regimes (MR-HIFU system). Top right: Corresponding heat sources: linear (top) and nonlinear (bottom; Karzova et al., 2018). Peak heating is 75 times higher with nonlinearity. Bottom: in HIFU therapy, an extracorporeal source is focused at a target location in the body and used to ablate tissue in a region about the size of a grain of rice.
60 | Acoustics Today | Fall 2019