A short phonon pulse injected into liquid $^{4}\text{H}\text{e}$ propagates away from the heater as a phonon sheet. The angular dependence of the energy flux has a mesa shape, i.e., a flat top, which is the phonon sheet, and steep sides. The mesa shape is caused by high energy phonon creation in the pulse along the symmetry axis; this depletes energy from the flux until the central portion of the pulse has a constant energy. The low energy phonons then occupy a thin sheetlike volume. We have measured the width of the phonon sheet from three heaters of different widths at different heater powers and distances from the heater. We find the remarkable result that the sheet width is inversely proportional to the width of the rectangular heater. Also the height of the mesa falls off as the inverse square of the distance from the heater. We present a phenomenological model for the phonon propagation in liquid helium at 0 bar, which predicts these dependencies. It also predicts that the sheet width is proportional to the heater pulse length, and is only a weak function of heater power, both of which are seen experimentally.