  We present a high-sensitivity measurement technique for mechanical
nanoresonators. Due to intrinsic nonlinear effects, different flexural modes of
a nanobeam can be coupled while driving each of them on resonance. This
mode-coupling scheme is dispersive and one mode resonance shifts with respect
to the motional amplitude of the other. The same idea can be implemented on a
{\it single} mode, exciting it with two slightly detuned signals. This two-tone
scheme is used here to measure the resonance lineshape of one mode through a
frequency shift in the response of the device. The method acts as an
amplitude-to-frequency transduction which ultimately suffers only from phase
noise of the local oscillator used and of the nanomechanical device itself. We
also present a theory which reproduces the data without free parameters.
