Abstract
Abstract
Highlights
Focusing small-amplitude acoustic waves with an array of transducers is commonly achieved through time-delay focusing and is termed ‘transmit beamforming’ (Szabo 2014)
The vapour bubble dynamics is not important for the time-delay focusing because the gas–liquid interface velocity is considerably slower than the shock wave
We observe that the speed of propagation is essentially constant with a speed of approximately 1700 m s−1. This will drop to the acoustic speed of approximately 1500 m s−1, yet the slow decay is due to the effective 2-D geometry where the shock velocity in the liquid decays as 1/r (Veysset et al 2018), in contrast with the 3-D case that scales as 1/r2
Summary
Focusing small-amplitude acoustic waves with an array of transducers is commonly achieved through time-delay focusing and is termed ‘transmit beamforming’ (Szabo 2014). Focusing of finite-amplitude waves at a fixed location has been achieved with a single transducer bonded to a spherically shaped surface. Chan, Hies & Ohl (2016) and Melde et al (2016) demonstrated that the waveform and location of the focus of acoustic waves can be altered with arbitrarily shaped surfaces using three-dimensional (3-D) printing. We demonstrate time-delay focusing for transient finite-amplitude waves with a variable focus. Note that here we assumed linear superposition of the acoustic transient waves
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