For a very short (t_p<0.25 mu s) Joule heating pulse in a metal film heater submerged in liquid ⁴He at low temperatures (T<0.1 K), the phonons created in the liquid separate into distinct low-frequency and high-frequency distributions. Phonons of intermediate frequencies are absent from the signal because they spontaneously decay to lower frequencies. High-frequency phonons above the decay cut-off ( omega > omega _c^{( infinity})) are stable as T to 0. We find that for a heater power of 10 mW mm^-2, these high-frequency phonons are not distributed over the available frequency range up to the maxon, but are concentrated in a narrow band around omega _c^{( infinity}). Times of flight show that the distribution of high-frequency phonons depends upon pressure P such that the peak is always at the pressure dependent decay cut-off omega _c^{( infinity})(P). We suggest that the majority of these detected high-frequency phonons are produced in the liquid ⁴He by frequency up scattering processes amongst the injected phonons.