Pressure shifts of the hyperfine splitting in Na 3(2)S((1/2)) that are due to buffer gases have been measured for the first time to our knowledge by all-optical means using the method of synchronized-quantum-beat spectroscopy reported previously [Y. Fukuda et al., Opt. Commun. 38, 357 (1981)]. The substate coherence is excited and detected with amplitude-modulated mode-locked laser pulses tuned to the D(1) line (pulse-repetition frequency, f(p); modulation frequency, f(m)), and the resonances observed at f(0) = nf(p) + ńf(m), (n and n' are integers) are used for the measurement. The pressure-shift coefficients obtained at 210 degrees C are 82, 61, -1, and -47 Hz/Torr for He, N(2), Ar, and Kr, respectively, within an accuracy of +/-3 Hz/Torr.