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Which of the following statements are true for wave motion?
A. Mechanical transverse waves can be propagate through all mediums
B. Longitudinal waves can propagate through solids only
C. Mechanical transverse waves can propagate through solids only
D. Longitudinal waves can propagate through vacuum

Answer
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Hint: Propagation depends on the property of the medium. Mechanical waves are a type of wave. Remember solid has a definite shape and its molecules are compactly bound to each other by some kind of force.

Complete Step-by-Step solution:
Mechanical transverse waves can propagate through solids only because transverse waves are shear waves, which move perpendicular to direction of propagation. Now we will see more detail about it.
Waves are of two kinds. One of the types is mechanical waves. Under mechanical waves there are another two types, the first is transverse wave and another is longitudinal wave.
First we will see what is a mechanical wave and then a transverse wave. Mechanical wave: It is a disturbance which transmits from one to another part in medium with constant speed by periodic oscillation of particle. The speed i.e. propagation depends on density and elasticity of medium. Transverse wave: The motion in which the particle of medium vibrates in a direction perpendicular to the direction of the wave's propagation. We know that solids have enough shear strength. The force present in solid is shear strength that holds solid together. While shear strength is less in liquid similarly for gases. That’s why Mechanical transverse waves can propagate through solids.

Correct option is C.

Note: Remember that all the transverse waves need not require a solid medium to propagate. Transverse wave can pass through the surface tension of the ocean. Waves which do not require medium are known as electromagnetic waves.