Fig. 2: Sound transmission through encapsulated microbubble-doped gel.
From: Observation of a transition to a localized ultrasonic phase in soft matter
a Sound level SL (referenced to a water measurement) versus frequency f for an undoped sample (open black circles), and three doped samples with encapsulated microbubble (EMB) volume fractions ϕ = 1.2% (solid green triangles), ϕ = 2.7 ± 0.5% (open blue squares), and ϕ = 9.9 ± 1.8% (solid gray diamonds). Several low-f thickness modes are indicated. The shaded yellow region highlights the anticipated EMB resonance frequency range. A correction factor is applied to the data to account for the finite sample thickness: −0.64 dB for the undoped sample and −0.36 dB for the doped samples. b Attenuation coefficient α versus f for the undoped sample and two doped samples from (a). Dashed lines and arrows indicate the frequency ranges for the two localized phases, which are bounded by mobility edges (identified by attenuation peaks). c Ratio of the scattering mean free path lS to the wavelength λ versus f for the two doped samples in (b). The x-axis frequency range spans the anticipated range of EMB resonance frequencies. The black arrows indicate the mobility edges (corresponding to the indicated α peaks in b) d, α (left vertical axis) and change in the phase angle Δθ (right vertical axis) versus f for ϕ = 2.7%. Note, the α spectrum in (d) is the same spectrum shown in (b). The black arrows indicate the mobility edges.
