Post History

Assuming the ear protector is a linear system, it will attenuate the various frequencies in a pulse the same as it would a steady tone at each frequency.

An impulse is by definition short-lived, and contains a wide spectrum of frequencies.  Since the attenuation as a function of frequency varies, there is no easy single number for the attenuation of an impulse.  This depends on the frequency content of the impulse.

Even for continuous tones, a single attenuation number is a dumbed-down rating.  I haven't looked at standards for hearing protection specs, but that single spec probably implies a particular frequency mix, and the attenuation at different frequencies may be weighed differently.  Very likely, different standards agencies have different specs for this too.

It is a lot easier, and results in more reliable numbers, for manufacturers to test sound attenuation devices one frequency at a time.  This is probably done with a slow frequency sweep.  Surely they have a nice graph internally that shows attenuation as a function of frequency.  Simpler specs are then derived from that.

If you had the graph and knew the frequency content of your "impulse", then you could compute some overall attenuation metric for that impulse.  However, the next impulse could have a different frequency mix, and therefore a different overall attenuation.  Without some definition of a standard impulse (a real mathematical impulse lasts 0 time and contains all frequencies equally), any impulse spec would be meaningless, and not particularly applicable to other impulses anyway.