Question

Why the longitudinal waves move faster through solids than transverse waves?​

Answer 1

As a generality, the speed of a wave is sqrt(elasticity/inertia), and for a wave in a 3D medium, that's sqrt(Elastic modulus/density).

The elastic modulus for transverse waves (such as earthquake S-waves) is the shear modulus
μ
, because the stress in a transverse wave is pure shear.

The elastic modulus for longitudinal waves (such as earthquake P-waves) is neither the bulk modulus K (for equal compression in three dimensions) or the Young's modulus E (for tension in one dimension but spontaneous shrinkage in the two others, as with a stretched wire) but a special P-wave modulus M (for pure compression in one direction only). This turns out to be equal to +4/3
K
+
4
μ
/
3
, which is automatically more than
μ
because of the 4/3, and in fact a lot more because
K
is usually several times bigger than
μ
- things are harder to compress than they are to shear.

Answer 2

No, longitudinal waves travel faster than transverse waves. The longitudinal wave transmission is faster than transverse wave transmission. This speed difference between the longitudinal and transverse wave can be noticed during an earthquake. During an earthquake, both longitudinal and transverse waves are produced. The initial tremor before the big tremor during an earthquake is longitudinal in nature and is called a P-wave. The big tremor after the initial tremor is called an S-wave.