Before reading this entry consider taking a look at this previous post that provides a basic overview regarding sound wave filters.
A band-pass filter is designed to pass all frequencies within a “passband” while attenuating or removing frequencies outside of that band.
These types of filters feature two important parameters: the center frequency and the bandwidth, which is sometimes controlled via a variable called “Q”. The bandwidth of the filter specifies how far from the center frequency the edge of the passband will reach.
It is important to keep in mind that “Q” is inversely proportional to the bandwidth. Therefore a high “Q” value is equivalent to a small bandwidth. Not all band-pass filters use “Q” to control bandwidth, some filters use controls that are directly proportional to the bandwidth.
The slope of the rate at which the frequencies below and above the cut-off frequencies are attenuated and removed varies depending on the order of the filter. Filters of higher order have steeper slopes. This means they are more effective at removing frequencies below and above the cut-off. To generated higher order filter effects, you can join multiple filters together in a serial configuration.
Here is a pd patch that I created to better understand how a low-pass filter works. This patch enables you to explore the interaction between sound waves of different frequencies with a low-pass filter. You can download it here.
Play around with this patch you will see how the amplitude of the sound continually decreases as the oscillator frequency is brought up further above the cut-off frequency. You can download it here.