  Gravitational wave production from bubble collisions was calculated in the
early nineties using numerical simulations. In this paper, we present an
alternative analytic estimate, relying on a different treatment of
stochasticity. In our approach, we provide a model for the bubble velocity
power spectrum, suitable for both detonations and deflagrations. From this, we
derive the anisotropic stress and analytically solve the gravitational wave
equation. We provide analytical formulae for the peak frequency and the shape
of the spectrum which we compare with numerical estimates. In contrast to the
previous analysis, we do not work in the envelope approximation. This paper
focuses on a particular source of gravitational waves from phase transitions.
In a companion article, we will add together the different sources of
gravitational wave signals from phase transitions: bubble collisions,
turbulence and magnetic fields and discuss the prospects for probing the
electroweak phase transition at LISA.
