Option 1 states that the speed of sound waves in a medium depends only on the elastic property of the medium and not on inertia. This statement is incorrect. The speed of sound waves in a medium depends on both the elastic property and inertia property of the medium. Elasticity refers to how well a medium can be compressed or stretched, while inertia refers to the resistance of a medium to changes in its state of motion. Both of these properties are important in determining the speed of sound waves in a medium.

Option 2 states that the speed of sound waves in a medium depends only on the inertia property of the medium and not on elastic property. This statement is also incorrect, as explained above.

Option 3 states that the speed of sound waves in a medium depends neither on its elastic property nor on its inertia property. This statement is incorrect, as the speed of sound waves in a medium depends on both properties.

The correct statement is option 4, which states that the speed of sound waves in a medium depends both on the elastic and inertia properties of the medium. Elasticity and inertia are both factors that influence the propagation of sound waves in a medium.