High quality observations of the low-degree acoustic modes (p-modes) exist for almost two complete solar cycles using the solar spectrophotometer Mark-I, located at the Observatorio del Teide (Tenerife, Spain) and operating now as part of the Birmingham Solar Oscillations Network (BiSON). We have performed a Fourier analysis of 30 calibrated time-series of one year duration covering a total period of 15 years between 1984 and 1999. Applying different techniques to the resulting power spectra, we study the signature of the solar activity changes on the low-degree p-modes. We show that the variation of the central frequencies and the total velocity power (TVP) changes. A new method of simultaneous fit is developed and a special effort has been made to study the frequency-dependence of the frequency shift. The results confirm a variation of the central frequencies of acoustic modes of about 0.45 mu Hz, peak-to-peak, on average for low degree modes between 2.5 and 3.7 mHz. The TVP is anti-correlated with the common activity indices with a decrease of about 20% between the minimum and the maximum of solar cycle 22. The results are compared with those obtained for intermediate degrees, using the LOWL data. The frequency shift is found to increase with the degree with a weak l-dependence similar to that of the inverse mode mass. This verifies earlier suggestions that near surface effects are predominant.