Mn(0.5)Zn(0.5)Dy(x)Fe(2-x)xO(4) (X <= 0.03) nanoparticles (NPs) were fabricated by using Ultrasonic irradiation using UZ SONOPULS HD 2070 ultrasonic homogenizer (frequency of 20 kHz and power of 70 W). Structural and morphological analyses were performed via XRD (X-ray powder diffractometer), TEM (Transmission electron microscopy) and SEM (Scanning electron microscopy). XRD presented the formation of Mn-Zn ferrite with average crystal size in 11 to 18 nm range. Direct optical energy band gaps (E-g) were specified applying diffuse reflectance investigations. E-g values are in a small band range of 1.61-1.67 eV. Low (10 K) and room temperature VSM data were recorded applying +/- 90 kOe external magnetic field. All samples exhibit superparamagnetic properties at RT. Magnetization parameters significantly increase due to coordination of Dy3+ rare earth ions. Magnetic moment per molecule (n(B)) increases from 0.952 mu(B) to 1.137 its and from 2.312 mu(B) to 2.547 mu(B) at RT and at 10 K data respectively. 10 K coercivity (H-e) values decrease from 260 Oe to 43 Oe. All samples have squareness ratios (SQR) of 0.231-0.400 range assigning the multi-domain structure at 10 K. ZFC-FC magnetization curves that were registered for two selected samples exhibit a divergence and a sharp drop below their T-peak positions. This event is typically correlated to the collective freezing of system and spin-glass-like phase. Real part AC susceptibility data slightly shift toward high temperature regions with increasing frequencies. Critical Slowing Down (CSD) model explained the spin dynamics of interacting NPs consistently with literature and proved the spin-glass behavior of samples at low temperatures.