A longitudinal vibration is a vibration in which the principal motion is in the direction of the longest dimension. [Rossing, Thomas D.; The Science of Sound; Addison-Wesley Publishing Company, 1982.]
A vibrating medium must lengthen and shorten 2 times per each lateral oscillation; so 1 longitudinal equals 2 lateral. Longitudinal frequencies are independent of string tension. [John Tyndall; Sound; Longmans, Green, and Co., London, 1893.]
Triple axis of the three modes of vibration drawn to reference a circle and sphere.
The three modes working together develop rotation by and through each other's motion - the rotation is the Rayleigh Wave or Surface Wave mode. The first two modes cause (or are) straight line and zig-zag motions only. The third or Rayleigh Wave is circular.
"Process for forming ambient temperature superconducting filaments."
Process for forming electrical conductors in the form of filaments which exhibit properties of electrical superconductivity at ambient or normal room temperature. From a scalar viewpoint the fineness of the filament conductors in insulating material severely limits the transverse (Hertzian) motion of electrons; thus limiting their mass movement and hence current losses. [U.S. Patent No. 4,325,795. Apr. 20, 1982.]
"On longitudinal correlations of the field of a light wave propagating in a medium having random inhomogeneities." [Radiophysics and Quantum Electronics." 13(7), July 1970. p. 834-835.]
"Magnetogravitational waves in a conducting isothermic atmosphere."
Among other things, the possibility of transforming longitudinal waves into transverse waves in the region of a strong magnetic field is indicated. This is important in building scalar wave detectors. [Zhugzhda is with the Institute of Terrestrial Magnetism, Ionosphere and Radio Wave Propagation. Astronomichsskiy Zhurnal (Moscow). 56(1), 1979. p. 74-83. In Russian.]
By the year 1821, Fresnel was able to show via mathematical methods that polarization could be explained by the wave theory of light and only if light was entirely transverse, with no longitudinal vibration whatsoever." https://en.wikipedia.org/wiki/Light#Wave_theory
Compression Wave Velocity
Figure 3.28 - Compression and Expansion Forces in Gyroscopic Motions
Figure 3.30 - Discrete Degrees or Steps in Gyroscopic Compression Motion
Figure 8.2 - Compression Wave Phase Illustration
Figure 8.3 - Coiled Spring showing Longitudinal Wave
Figure 9.11 - Compression Wave with expanded and contracted Orbits
Longitudinal Waves in Vacuum
12.31 - Heat Generated Through Resistance to Compression
16.09 - Positive Electricity is Compression