How many times faster is the speed of sound in the fluid compared to the peak amplitutde of the particle velocity

171500 times faster.

Explanation: First let's take our Fluid medium to be air. The speed of sound in air is 343m/s or 343000mm/s.

Now, particle velocity is that which shows the alternating mean velocity of a particle in a medium(say in this case air).

A particle of air exposed to a standard sound pressure of 1 Pascal as a peak velocity amplitude of about 2mm/s.

Recall that the value of speed of sound in Air when converted to mm/s is 343000mm/s.

To get the number of times it's faster than the peak particle Velocity of air. We have to divide it by peak particle Velocity of air which is 2mm/s.

343000/2

=171500 times faster.

I believe this is clear.