8.
A sound wave propagating in a solid block can have the following modes:
a. One transverse only
b. One longitudinal only
c. Two transverse and one longitudinal only
d. One transverse and one longitudinal only
Sound waves propagating in a solid block support two transverse modes and one longitudinal mode due to the solid’s ability to sustain shear and compressional deformations in three dimensions. The correct answer is option c. Two transverse and one longitudinal only.
Option Analysis
a. One transverse only: Incorrect, as solids support longitudinal waves alongside transverse ones; excluding longitudinal ignores compressional propagation.
b. One longitudinal only: Incorrect, since solids also allow transverse (shear) waves perpendicular to propagation, unlike fluids.
c. Two transverse and one longitudinal only: Correct. In a solid, one longitudinal mode has particle motion parallel to propagation, while two transverse (shear) modes exist—one in each perpendicular plane due to 3D shear rigidity.
d. One transverse and one longitudinal only: Incorrect, as it undercounts transverse polarizations; solids permit two independent shear directions.
Sound wave modes in solid block reveal why solids uniquely support multiple wave types. Unlike gases or liquids, solids propagate two transverse and one longitudinal modes due to shear modulus, making option c the precise answer for competitive exams.
Wave Propagation Basics
Longitudinal waves involve particle vibrations parallel to propagation, creating compressions like audio in air. Transverse waves feature perpendicular motion, possible only in solids with rigidity. In a solid block, three modes emerge: one longitudinal (P-wave) and two transverse (S-waves, vertically and horizontally polarized).
Why Two Transverse Modes?
Solids resist shear in two perpendicular directions, enabling two independent transverse polarizations. A single transverse option overlooks this 3D freedom, common in seismology or ultrasonics. Fluids lack shear strength, limiting them to one longitudinal mode.
Exam Relevance
For CSIR NET or JEE, recognize solids’ tri-modal support versus fluids’ mono-modal limit. Visual aids like particle diagrams clarify: longitudinal stretches along the path; transverses shear orthogonally.
