The angular distributions of high-energy phonons, that are created by a short pulse of low-energy phonons propagating in superfluid 4 He, are measured for different heater sizes and heater powers. We find that the intrinsic full width at half height of the high-energy phonons is proportional to the reciprocal of the width of the heater that creates the low-energy phonons. This is similar to the behavior shown by the low-energy phonons where the width of the phonon sheet is inversely proportional to the heater width. We discuss the correspondence between the formation of the phonon sheet by the low-energy phonons and the creation of high-energy phonons, and conclude that the phonon sheet is caused by the creation of high-energy phonons within a few millimeters of the heater. We also show that the total energy in the high-energy phonons increases linearly with heater power, once a threshold power is reached. This indicates that the initial low-energy phonons increase in number but not energy, as the heater power is increased.