#### Cousin Mose

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Long time lurker, first time poster.

In an interview at Erin's Audio Corner, Purifi co-founder Lars Risbo mentioned that a driver playing a narrow passband can generally produce higher SPL than the same driver playing a wider part of the spectrum. If this is true, there must be some mathematical relationship between bandwidth and sensitivity or power handling. Despite my best and dogged googling, I can't find such as formula. In fact, I can't find much of any discussion on the topic.

In electrical engineering terms, I believe I'm looking for the acoustic equivalent of the "gain-bandwidth product".

Does such a formula exist for loudspeakers? My reason for asking is that I have been contemplating speaker designs with mid-range and mid-bass woofers that only cover about 2 octaves each (a la Revel's Salon2), and I would like to have a way to reasonably estimate the SPLmax of a driver over such a narrow bandwidth (I believe published power ratings are typically based on weighted noise signals that span at least a decade).

The basic premise seems intuitive enough. If SPLmax of a driver is limited by excursion at low frequencies, then lowering the top end will have no effect. However, eliminating those excursion-limiting frequencies on the low end by raising the high-pass filter will allow the driver to play higher frequencies with the same Xmax. Since it is well known that increasing frequency with constant excursion produces higher SPL, this is clearly a case where the driver can play louder by narrowing the passband.

In other cases, the driver may be thermally limited at SPLmax. In such cases, narrowing the passband at either end necessarily reduces the total power handled by the driver (the driver is producing less sound, so it must be using less energy). This, in turn, allows the driver to handle more power in the remaining passband. Again, SPLmax has increased by narrowing the passband.

So, how can I accurately calculate SPLmax in my target passband based on power handling/sensitivity ratings from standardized test bandwidths?

Thanks you in advance for your contributions.

In an interview at Erin's Audio Corner, Purifi co-founder Lars Risbo mentioned that a driver playing a narrow passband can generally produce higher SPL than the same driver playing a wider part of the spectrum. If this is true, there must be some mathematical relationship between bandwidth and sensitivity or power handling. Despite my best and dogged googling, I can't find such as formula. In fact, I can't find much of any discussion on the topic.

In electrical engineering terms, I believe I'm looking for the acoustic equivalent of the "gain-bandwidth product".

Does such a formula exist for loudspeakers? My reason for asking is that I have been contemplating speaker designs with mid-range and mid-bass woofers that only cover about 2 octaves each (a la Revel's Salon2), and I would like to have a way to reasonably estimate the SPLmax of a driver over such a narrow bandwidth (I believe published power ratings are typically based on weighted noise signals that span at least a decade).

The basic premise seems intuitive enough. If SPLmax of a driver is limited by excursion at low frequencies, then lowering the top end will have no effect. However, eliminating those excursion-limiting frequencies on the low end by raising the high-pass filter will allow the driver to play higher frequencies with the same Xmax. Since it is well known that increasing frequency with constant excursion produces higher SPL, this is clearly a case where the driver can play louder by narrowing the passband.

In other cases, the driver may be thermally limited at SPLmax. In such cases, narrowing the passband at either end necessarily reduces the total power handled by the driver (the driver is producing less sound, so it must be using less energy). This, in turn, allows the driver to handle more power in the remaining passband. Again, SPLmax has increased by narrowing the passband.

So, how can I accurately calculate SPLmax in my target passband based on power handling/sensitivity ratings from standardized test bandwidths?

Thanks you in advance for your contributions.

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