We have recently introduced the mass-polariton (MP) theory of light to describe the coupled dynamics of the field and matter when a light pulse propagates in a transparent medium. The theory is based on combining the electrodynamics of continuous media and continuum mechanics, which are both widely used standard theories in their fields of physics. The MP theory shows that a light pulse propagating in a transparent medium is accompanied by a mass density wave (MDW) of atoms set in motion by the optical force density of the light pulse. In the corresponding quantum picture, the covariant coupled state of the field and matter is described as the MP quasiparticle, which has coupled field and medium components. We study a schematic experimental setup that would enable measurements of the atomic displacements and the excess mass density related to the MDW of a Gaussian MP pulse propagating in an optical fiber made of fused silica.