There are a number of factors that determine the sound of the bass guitar instrument. Sound shaping factors are those which control Equalization, Compression, Reflections, Effects, Filtering, and other digital signal processing.
(For more information on digital effects check out easy-home-recording.com). Some of the signal processing for the bass is intentional, while others are unwanted, like the effect of a bad or cheap guitar cord from the bass to the amp, or an improperly vented speaker cabinet.
Having a good understanding of the Frequency Spectrum is helpful in understanding the basics of sound shaping. Among the more important factors are the frequency equalization effects, or EQ for short. Your old stereo had these as tone controls labeled Bass and Treble, or Lows and Highs.
These are primitive tone controls, which are now standard on not only the amplifier for your bass but on the bass itself (usually active pickup controls). Even the older Fender Precision and Jazz Bass had a tone control knob, which rolled off the high frequencies of the instrument.
There are a number of bass players (and sound men) who are in the dark about getting a good EQ for the bass. There are frequencies that are highly desirable to boost and there are frequencies to avoid. See the page on Equalization for recommendations to bass players.
The other important component is the sound pressure level. This is usually measured in decibels or dB for shorthand. Decibels are a measurement or indication of energy for the sound. The scale for this measurement is logarithmic (log10 for mathematics guys) and not linear.
For example, a speaker which is putting out a 95db sound level has 50% more energy than a 92db sound level. Sound levels above 150db are considered life-threatening. Sound levels above 140db are considered painful. Jet engines and rock concerts often approach 130db.
However, to the musician, the most common measurement of sound volume, is the watt, because this is what is used to rate the amplifiers and speakers. Speakers are measured in watts and in SPL (Sound Pressure Level in db’s).
Be sure to see the Speakers page, because there are significant ways of getting more volume from your system by simply changing the speakers or the cabinet design.