  The paper focuses on applying the octonions to explore the electromagnetic
and gravitational equations in the presence of some material media, exploring
the frequencies of astrophysical jets. Maxwell was the first to use the algebra
of quaternions to describe the electromagnetic equations. This method
encourages scholars in adopting the quaternions and octonions to study the
physical properties of electromagnetic and gravitational fields, including the
field strength, field source, linear momentum, and angular momentum and so
forth. In the paper, the field strength and angular momentum in the vacuum can
be combined together to become one new physical quantity, that is, the
composite field strength within the material media. Substituting the latter for
the field strength in the vacuum will deduce the field equations within
material media, including the electromagnetic and gravitational equations in
the presence of some material media. In terms of the electromagnetic fields,
the electromagnetic equations in the presence of some electromagnetic media are
able to explore a few new physical properties of electromagnetic media.
Especially, in case the magnetic flux density and magnetization intensity both
fluctuate at a single-frequency, their frequencies must be identical to each
other within electromagnetic media. In some extreme cases, the electromagnetic
equations within electromagnetic media will be degenerated into the Maxwell's
equations in the vacuum. The above reveals that the electromagnetic equations
within electromagnetic media are capable of extending the scope of application
of electromagnetic theory. For the gravitational fields, there are some similar
inferences and conclusions within gravitational media. Further they can be
utilized to research the frequencies of astrophysical jets.
