A short phonon pulse injected into liquid 4 He 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.

We have measured the pressure dependence of a single phonon sheet and the interaction of two such sheets, in pure liquid 4 He, from 0 to 21 bar and show it is dominated by three phonon processes ͑3pp͒. Pressure affects the 3pp scattering by changing the shape of the dispersion curve. The scattering varies from very strong at P = 0 to zero at P = 19 bar. The 3pp is small angle scattering at P = 0 and, as pressure is increased, the angles decrease further and eventually become zero. We find that the signal from a single phonon sheet increases considerably with pressure to a maximum at P = 7.5 bar and then decreases to a minimum at ϳ15 bar, and becomes independent of pressure at Ͼ19 bar. We discuss this behavior in terms of the creation of high-energy phonons and the expansion of the phonon sheet. The signal from the collision of two sheets, at 8.8°to each other, depends on the pressure dependences of the energy density in the individual sheets and of the 3pp. This gives direct evidence that the interaction between two phonon sheets is caused by 3pp scattering. Theory relevant to this experiment is given in the paper following this one, see Adamenko et al., Phys. Rev. B 72, 054507 ͑2005͒.

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