Picosecond ultrasonics, which studies laser-induced high-frequency strain waves, is a reliable and versatile method for nondestructive materials' characterization. Strain waves are generated through a light interaction with charges and their subsequent relaxation, and these waves conceal a wealth of information on the material. However, strain waves are detected through their convolution with a sensitivity function, which blurs much of this information. Here, we show that the reflection of strain waves at a free surface leads to the appearance of a Fano resonance in the reflectivity spectrum, accompanied by a drastic increase in the detection bandwidth. We take advantage of this feature to provide a method for the reconstruction of strain waves. We apply it to unambiguously highlight the exact origin of the generation of coherent acoustic phonons in Stranski-Krastanov grown quantum dots, revealing that both the wetting layer and quantum dots are responsible for the generation. Our results will offer the possibility to understand better the interaction of light with charges and their interactions with the lattice.