  Some high-resolution observations have revealed that the active-region solar
corona is filled with myriads of thin strands even in apparently uniform
regions with no resolved loops. This fine structure can host collective
oscillations involving a large portion of the corona due to the coupling of the
motions of the neighbouring strands. We study these vibrations and the possible
observational effects. Here we theoretically investigate the collective
oscillations inherent to the fine structure of the corona. We have called them
fundamental vibrations because they cannot exist in a uniform medium. We use
the T-matrix technique to find the normal modes of random arrangements of
parallel strands. We consider an increasing number of tubes to understand the
vibrations of a huge number of tubes of a large portion of the corona. We
additionally generate synthetic time-distance Doppler and line broadening
diagrams of the vibrations of a coronal region to compare with observations. We
have found that the fundamental vibrations are in the form of clusters of tubes
where not all the tubes participate in the collective mode. The periods are
distributed over a wide band of values. The width of the band increases with
the number of strands but rapidly reaches an approximately constant value. The
frequency band associated with the fine structure of the corona depends on the
minimum separation between strands. We have found that the coupling between the
strands is of large extent. The synthetic Dopplergrams and line-broadening maps
show signatures of collective vibrations, not present in the case of purely
random individual kink vibrations. We conclude that the fundamental vibrations
of the corona can contribute to the energy budget of the corona and they may
have an observational signature.
