Two 1/f noise peaks were found in a carbon soot resistor at voltages characteristic of Kohn anomalies in graphite. The ratio of the electron-phonon coupling matrix elements at the anomalies calculated from the noise peak intensities is the same as the one obtained from the Raman frequencies. This demonstrates that the electron-phonon coupling is the microscopic source of 1/f noise in carbon soot. A new, very general formula was deduced for the frequency exponent, wherein nonlinearity and dispersion are the only ingredients. The interplay between nonlinearity and dispersion in this formula describes the sublinear-supralinear transitions experimentally observed at both anomalies in the voltage dependence of the frequency exponent. A quadratic dependence of the 1/f noise parameter on the matrix element is proposed and applied to explain the M-shape of the 1/f noise in graphene. We found that the frequency exponent mimics the dependence of the noise intensity in the whole voltage range, while both are the image of the graphite phonon spectrum. This implies that the source of nonlinearity is in the electron-phonon coupling which modulates the slope of the spectrum. It requires the presence of 1/f noise in the thermal noise background of the resistor till phonon frequencies.