The aim of the present study is to investigate the effect of a single partition and double partitions between the main vehicle cabin and the engine bay cavity, including the effect of mismatch in acoustic impedances. Imposing a partial vacuum condition inside the double walled partition between the main compartment and the engine bay creates the characteristic impedance mismatch. Numerical simulations are conducted to study the effect of various design parameters on the acoustic transmission. The SPL (Sound Pressure Level) at the driver's ear position is monitored. The source of structure born noise is considered to be a harmonic excitation transmitted via the engine block mounts. The influence of the double partition by the engine and the partial vacuum condition in the enclosed gap on the SPL at the driver's ear is very complex and highly non-linear. The main conclusions from the present investigation are as follows: 1. The double partition by the engine with or without partial vacuum in the gap does not reduce the interior SPL at the driver's ear at all frequencies. However, for specific excitation frequencies this passive approach could reduce the SPL up to 32dB. 2. A single partition by the engine combined with a double partition between the main cabin and the luggage compartment is very effective at reducing the SPL at the driver's ear across the frequency range 30-170Hz. The recorded reduction in SPL for some frequencies is in the range 5-46dB. This partition would add around 2.5 kg to the vehicle weight and could be included in the structure of the rear seats. 3. The comparison between different materials shows that the wooden partition between the engine bay and the car compartment reduces the SPL in a large proportion of the frequency range considered, e.g. 35-75Hz and 120-200Hz.