  Dealing with the inverse source problem for the scalar wave equation, we have
shown recently that we can reconstruct the space-time dependent source function
from the measurement of the wave, collected at a single point $x$ for a large
enough interval of time, generated by a small scaled droplets, enjoying large
contrasts of its bulk modulus, injected inside the domain to image. Here, we
extend this result to reconstruct not only the source function but also the
variable wave speed. Indeed, from the measured waves, we first localize the
internal values of the travel-time function by looking at the behavior of this
collected wave in terms of time. Then from the Eikonal equation, we recover the
wave speed. Second, we recover the internal values of the wave generated only
by the background (in the absence of the small droplets) from the same measured
data by inverting a Volterra integral operator of the second kind. From this
reconstructed wave, we recover the source function at the expense of a
numerical differentiation.
