It Is Assumed to Date That the Energy Source of Azimuthal Small-Scale Ulf Waves In the Magnetosphere (Azimuthal Wave Numbers M1) Is Provided By the Energetic Particles Interacting With the Waves Through the Bounce-Drift Resonance. In This Paper We Have Solved the Problem of the Bounce-Drift Instability Influence on the Spatio-Temporal Structure of Alfven Waves Excited By a Source of the Type of ´ Sudden Impulse In a Dipole-Like Magnetosphere. It Is Shown That the Impulse-Generated Alfven Oscillation Within a Time ´ Τ∼Mt N (Where T N Is the Toroidal Eigenfrequency) Is a Poloidal One, and Each Field Line Oscillates With Its Own Eigenfrequency That Coincides With the Poloidal Frequency of a Given L-Shell. As Time Elapses, the Wave Becomes Toroidally Polarized Because of the Phase Difference of the Disturbance, and the Oscillation Frequency of Field Lines Tends to the Toroidal Frequency.