Ion heating effects by a non-monochromatic r.f. near the lower hybrid frequency with slowly varying amplitude are investigated experimentally in a low density argon plasma. Temporal measurements of the ion velocity distribution function show different time evolution of ion energy, depending on the frequency spectra of the r.f. signal. When the r.f. is (balanced-) amplitude-modulated with noise, the heating effect on ions is more dominant than the cases of the monochromatic r.f. and the frequency-modulated r.f. For the sinusoidal amplitude modulation, maximum broadening of the ion velocity distribution function is observed when envelope of the amplitude varies near the ion cyclotron frequency, which qualitatively agrees with the theoretically expected behaviour. From simple analysis of single particle motion, it is suggested that ion heating may be caused by a low frequency oscillation driven by an oscillating collective ponderomotive force which is originally produced by the non-uniform r.f. electric field with slowly varying amplitude.