How many psychoacoustical critical bands are there? I understand that the human ear works as a band-pass filter and I have doubt regarding the number of such bandpass filters in the filter bank.

I came across these two possible explanations of how it happens:


There are no fixed bands and the critical bandwidth of a sound depends on which audio frequency the ear is exposed to. In such a case, the audio frequency could be treated as the center frequency of a bandpass filter and another frequency occurring in the same band gets masked out. 
There are 24 fixed bandpass filters with their corresponding fixed bandwidths independent of the audio frequency the ear is exposed to. In such a case too, frequencies occurring in the same band sound like a single frequency and the difference goes undetected.


Which one of them is correct? Do the critical bands exist only between the 24 fixed values or are they continuous values?
Neither. The basilar membrane in your ear performs a frequency-to-place transformation which is then picked up by an array of thousands of hair cells (cilia). Therefore there are thousands of heavily overlapped bands. The processing that follows is very complex and not completely understood. The shape of the effective band pass filter at each location on the membrane can be measured in animals, and the masking curves can be measured by listening tests. Masking is measured by increasing the amplitude of a test tone relative to the masking tone until it is audible, so the situation is a bit different that what you assumed in your question (where you assumed that if the masker and the test tone were in the same band, you only hear one tone). The actual result is that as the test tone approaches the masker frequency, it must have a higher amplitude before it can be detected. 

Bob