Detection of Acoustic signals
Building a bandpass filter by combining a high pass section and a low pass section is feasible if the desired bandpass is relatively high compared to the center frequency. This simplifies the design since it means that the high pass and low pass sections will not interfere with each other since they will be relatively far apart in frequency.  In terms of Q (which is defined as the center frequency divided by the bandwidth), this is a low Q filter. You didn't provide any information about the bandwidth of the signal you are trying to detect.  This is important in determining the bandwidth of your filter. You also didn't give the expected level of your signal. This is important in determining what sensitivity your receiver needs. The lower the expected level, the more significant is background noise. The purpose of the filter is to lower the background noise level so the required bandwidth is function of these parameters. Assuming the signal level is not buried in the background noise, you can probably get away with using separate high and low pass filters.  If the signal level is low then you may need to build a much narrower bandwidth filter (high Q) which will require a more sophisticated design.