In both cases the amplitude of the oscillations decreases more or less rapidly.
(25) The sum of the disturbance is obtained by adding (24) and (25) y = y l +y 2 = 2a cos Ut s i n 57 x, (26) At any given instant t this is a sine curve of amplitude 2a cos (27r/A)Ut, and of wave-length A, and with nodes at x = o, a A, A, ..., that is, there is no displacement at these nodes whatever the value of t, and between them the displacement is always a sine curve, but of amplitude varying between +2a and - 2a.
Thus Mach found an amplitude 0 2 cm.
The 12-hour term is much less variable, especially as regards its phase angle; its amplitude shows distinct maxima near the equinoxes.
Each section then vibrates, and its amplitude goes through all its values in time given by 21rUT/A =2r, or T =A/U, and the frequency is U/A.