Intense electrostatic waves of short wavelength are frequently observed upstream of the earth's bow shock. These waves are very impulsive, and their peak amplitudes correlate strongly with the temporal flux profiles of simultaneously observed energetic ions and electrons which are reflected from the shock. Our paper suggests an explanation of this broadband electrostatic noise in terms of electron acoustic waves driven unstable by the ion and/or electrom beams. These waves do not exist in thermodynamic equilibrium plasma and therefore require nonthermal distributions for their occurrence. A simple model is developed for finite temperature beam and background particles with Maxwellian or Lorentzian distributions. The beam-associated instability can be classified as being due to Landau resonance or negative wave energy. Depending on the plasma parameters the mode discussed here naturally extends and links to the ion acoustic wave or electron plasma oscillation. A numerical parameter study is provided for various beam plasma situations. The frequency theoretically obtained ranges between the ion and the electron plasma frequency, and the wavelength amounts to several Debye lengths for maximum growth. Since the beam mode has a linear dispersion relation, the Doppler-shifted frequency in the spacecraft frame should depend linearly on the beam velocity and on the wave vector as well. It is anticipated that these characteristics may allow parts of the observed broadband high-frequency noise to be identified as beam-driven electron acoustic waves.