Question

Why a solid substance is able to transport both longitudinal waves and transverse waves, but a homogeneous fluid is able to transport only longitudinal waves?

Short answer

Longitudinal waves depend on the compressibility of the fluid for their propagation. Transverse waves require a restoring force in response to shear strain., that solid can provide therefore solid substance is able to transport both longitudinal and transverse waves.

Step-by-step solution

Definition of transverse and longitudinal wave

A transverse wave is one in which the elements of the medium move in a direction perpendicular to the direction of propagation.

A longitudinal wave is one in which the elements of the medium move in a direction parallel to the direction of propagation.

Explanation

Longitudinal waves depend on the compressibility of the fluid for their propagation. Transverse waves require a restoring force in response to shear strain. Fluids do not have the underlying structure to supply such a force. A fluid cannot support static shear. A viscous fluid can temporarily be put under shear, but the higher its viscosity the more quickly it converts kinetic energy into internal energy. A local vibration imposed on it is strongly damped, and not a source of wave propagation.

So that solid substance is able to transport both longitudinal waves and transverse waves, but a homogeneous fluid is able to transport only longitudinal waves