Tyre cavity noise is a narrow band, high amplitude resonance which occurs when the sound waves in a car tyre oscillate back and forth in one direction with a low loss factor. Manufacturers add damping materials to vehicles, due to the difficulty of reducing the source noise, or mitigating the transmission path from wheel hub to the interior, as part of reducing the overall structure borne noise. When the wheel is rolling, the Doppler effect leads to two characteristic cavity resonance frequencies, which change with speed, loading and temperature. If these couple with a suspension component resonance, a transmission path to the cabin can result. One method to attenuate the sound is by using passive resonators, such as Helmholtz and quarter wavelength resonators. Here, a rapid design method is developed, based around one-dimensional waveguide equations in order to optimise the dimensions and thus the tuned resonant frequency of the wheel based Helmholtz resonators.With three tuned resonators, a reduction in the peak sound amplitude from 103 to 88 dB is possible, over a speed range from 54 km/h to 108 km/h. With five resonators, a reduction from 103 to approximately 87 dB is shown. Thus, the larger number of resonators is better able to attenuate the cavity noise over a larger frequency range.