Influence of wave noise on frequencies and amplitudes of the solar p-modes

The influence of space- and time-dependent random mass density field, that is associated with granules, on frequencies and amplitudes of the solar {\it p}-modes is examined in the limit of weak random fields and small amplitude oscillations. The $p$-modes are approximated by the sound waves which propagate in the gravity-free medium. Using a perturbative method, we derive a dispersion relation which is solved for the case of wave noise for which the spectrum $E(k,\omega)\sim E(k) \delta(\omega-c_{\rm r}k)$, where $\delta$ is the Dirac's delta-function and $c_{\rm r}$ is the random phase speed. We find that at $c_{\rm r}=\omega/k$ {\bf a} resonance occurs at which the cyclic frequency $\omega$ tends to infinity. For values of $c_{\rm r}$ which are close to the resonance point, the frequency shift may be both negative or positive and the imaginary part of the frequency attains the negative (positive) sign for $c_{\rm r}<\omega/k$ ($c_{\rm r}>\omega/k$).