This article deals with the problem of the statistical performance analysis of the MUSIC ( Multiple Signal Classification ) algorithm which is an eigen decomposition based method for the estimation of the angles of arrival of signals received by an array of sensors. In past work the performance of the MUSIC algorithm was studied ( via an asymptotic statistical analysis of the null spectrum of the algorithm ) for the case of two plane waves of equal power in noise. In this article, a new theoretical formula is derived for the signal to noise ratio resolution threshold of two uncorrelated, narrow band plane waves with equal powers in angular sectors received by an array of sensors. The accuracy of the formula is assessed using examples which compute the theoretical signal to noise ratio resolution threshold and compare it with the threshold obtained from simulations.