What makes the neurons of the auditory nerve with such high-speed?
High Speed vs High Frequency
For starters, what you are describing is a high frequency signal, not necessarily a high speed signal.  High speed signals are caused by myelination (a sheath of fat deposits that encases neuron fibers), and by minimizing the number of actual dendrite/Axon junctions you need to pass through to get from point A to point B.  In this respect, the nerves responsible for muscle control tend to be very long and have similar myelination to the cells in your ear; so, muscle control neurons would if anything transfer a signal faster than the more densely packed neurons in your ear.
Now to Answer the actual question: Why the Higher Frequency?
No one nerve in your ear actually needs to transmit a signal at a higher frequency than those nerves used by muscles.   Instead you have a number of different nerves detecting for different audio frequencies, and your brain then receives a combination of signals that tell it that various Audio Frequencies are being detected 1.  Each of the hairs in your inner ear tapers from the base to the apex such that the apex begins being stimulated by low frequencies, but the base only begins being stimulated by higher frequencies 2.
Each auditory nerve fiber is actually a cluster of nerves that work together at different frequencies to create a more complex signal. This results in a number of parallel signals that is interpreted as a complex (high frequency) signal.
Here is a simple diagram showing how low frequency signals can merge to make a higher apparent frequency.