Acoustic "phase shift" methods have been used in the past to accurately measure the sound speed of gases. In this work, a phase shift method for measuring the sound speed of gases over small path lengths is presented. We have called this method the discrete acoustic wave and phase detection (DAWPD) method. Experimental results show that the DAWPD method gives accurate (+/-3.2 ms) and predictable measurements that closely match theory. The sources of uncertainty in the DAWPD method are examined and it is found that ultrasonic reflections and changes in the frequency ratio of the transducers (the ratio of driving frequency to resonant frequency) can be major sources of error. Experimentally, it is shown how these sources of uncertainty can be minimized.