(a) Give reason why transverse waves can be propagated in solids,
(b) Give reason why longitudinal waves can be propagated through all the three types of media - solids, liquids and gases.
(c) Describe in brief about two types of waves that can be propagated on the free surface of water.

Explanation

(a) In order to have propagation of transverse waves, we need to produce crests and troughs. Tor this we need to produce shearing strain whereby we can change the shape of a medium. For this to happen, medium selected for the propagation of transverse waves, must be capable enough to sustain shearing stress i.e. They must have very high value of modulus of rigidity. Now we know that solids have very high value of modulus of rigidity. Hence transverse waves can be propagated in solids.
(b) Longitudinal waves propagate in the form of condensations and rarefactions, causing changes in density and pressure. Accordingly, compressive and expansive stresses are produced. All the three media - solids, liquids and gases can sustain compressive and expansive stresses and so longitudinal waves can be propagated in all of these media.
(c) Two types of waves which can propagate on free surface of water (i.e, on the uppermost layer of water which is in contact with atmosphere) are capillary waves and gravity waves.

(i) Capillary waves : They are transverse waves of fairly short wavelengths (few centimeter only). Here necessary restoring force is produced due to surface tension property of water.
(ii) Gravity waves : They are transverse as well as longitudinal in nature. They have large wave lengths ranging from several meters to several hundred meters. Here necessary restoring force is produced by the pull of gravity, which compels water surface to remain at lowest possible level. During the propagation of these waves on the free surface of water all the particles of water medium, from surface to the bottom oscillate with gradually decreasing amplitude Here particles of water medium oscillate up and down as well as back and forth. The waves in an ocean are the combination (superposition) of transverse and longitudinal waves.
Transverse and longitudinal waves are found to be travelling with different speeds even in the same solid medium (because for a given solid medium, its shear modulus and bulk modulus are different.)