The natural frequency of free longitudinal vibrations refers to the frequency at which an object vibrates when it is free to move without any external forces acting on it. The natural frequency depends on various factors such as the mass of the object, the stiffness of the material, and the length of the object.

The correct answer is option 'D' which states that the natural frequency is equal to all of the mentioned quantities. Let's analyze each option to understand why it is correct:

a) 1/2π√s/m:
This equation represents the natural frequency in terms of stiffness (s) and mass (m). The square root of the ratio of stiffness to mass determines the frequency. As stiffness increases, the natural frequency also increases. Similarly, as mass increases, the natural frequency decreases. Hence, this option is correct.

b) 1/2π√g/δ:
This equation represents the natural frequency in terms of gravitational acceleration (g) and the density of the material (δ). The square root of the ratio of gravitational acceleration to density determines the frequency. As gravitational acceleration increases, the natural frequency decreases. Similarly, as density increases, the natural frequency decreases. Hence, this option is also correct.

c) 0.4985/δ:
This option provides a specific value for the natural frequency and does not take into account any other factors such as stiffness or mass. Hence, it cannot be considered as the correct answer.

d) All of the mentioned:
This option includes both option 'a' and option 'b', which are correct explanations for the natural frequency. Therefore, option 'D' is the correct answer as it considers all the mentioned factors in determining the natural frequency of free longitudinal vibrations.