Final answer:
The bassoon is the lowest-sounding member of the double-reed family, producing lower frequencies due to its length. The bass clarinet uses a single reed and is not in the double-reed family.
Step-by-step explanation:
The lowest-sounding member of the double-reed family is the bassoon. This is because the bassoon is significantly longer than the other double-reed instruments listed, allowing it to produce lower frequencies. While the oboe and English horn have higher pitch ranges, the bass clarinet technically is not a member of the double-reed family as it uses a single reed. To give more insight into the acoustic qualities of these instruments, a bassoon with a fundamental frequency of 90.0 Hz would have overtones that depend on its shape and construction, which can be complex due to the double reed affecting the harmonics. In this example, for a simple model where the bassoon acts like a tube open at both ends, the first three overtones would be at integer multiples of the fundamental frequency (180 Hz, 270 Hz, 360 Hz) although in reality, it is more similar to a tube closed at one end.