The Doppler effect is a shift in the frequency of waves emitted from an object moving relative to the observer. By observing and analysing the Doppler shift in electromagnetic waves from astronomical objects, astronomers gain greater insight into the structure and operation of our Universe. In this paper, a simple technique is described for teaching the basics of the Doppler effect to undergraduate astrophysics students using acoustic waves. An advantage of the technique is that it produces a visual representation of the acoustic Doppler shift. The equipment comprises a 40 kHz acoustic transmitter and a microphone. The sound is bounced off a computer fan and the signal collected by a DrDAQ ADC and processed by a spectrum analyser. Widening of the spectrum is observed as the fan power supply potential is increased from 4 to 12 V.