  We propose a new family of high-order explicit generalized-$\alpha$ methods
for hyperbolic problems with the feature of dissipation control. Our approach
delivers $2k,\, \left(k \in \mathbb{N}\right)$ accuracy order in time by
solving $k$ matrix systems explicitly and updating the other $2k$ variables at
each time-step. The user can control the numerical dissipation in the discrete
spectrum's high-frequency regions by adjusting the method's coefficients. We
study the method's spectrum behaviour and show that the CFL condition is
independent of the accuracy order. The stability region remains invariant while
we increase the accuracy order. Next, we exploit efficient preconditioners for
the isogeometric matrix to minimize the computational cost. These
preconditioners use a diagonal-scaled Kronecker product of univariate
parametric mass matrices; they have a robust performance with respect to the
spline degree and the mesh size, and their decomposition structure implies that
their application is faster than a matrix-vector product involving the
fully-assembled mass matrix. Our high-order schemes require simple
modifications of the available implementations of the generalized-$\alpha$
method. Finally, we present numerical examples demonstrating the methodology's
performance regarding single- and multi-patch IGA discretizations.
