Natural frequency of a body depends upon both inertia and elastic properties of the material of the body.

For natural oscillation, a system must possess two quantities such as elasticity and inertia. If system is displaced from its equilibrium position, then the elasticity provides a restoring force to the system to reach equilibrium. The property of inertia brings the system to the overshoot equilibrium. This regular show between the elastic and inertia properties allows oscillatory motion to occur.

Simple harmonic motion requires a restoring force, as that brings the objects back to the equilibrium position.

Restoring force requires inertia to keep the object in motion throughout the equilibrium, which results in simple harmonic motion.

Inertia requires elasticity that results in the spring constant.

Vibrations in spring are only possible without the involvement of gravity. This is not required for spring motion; but for pendulum harmonic motion it may be essential, so it cannot be an example of perfect simple harmonic motion.

So, gravity is not necessary component for the simple harmonic motion.

For a simple harmonic oscillator, Force acting should be directly proportional to the displacement from the mean position and in opposite direction.

Let the force acting be F and displacement be x, then  for simple harmonic motion. This means that there should be restoring force acting on the body.Hence, the correct answer is B

The temperature of nearby air molecules doesn’t seem to affect the frequency of the string. Hence, option D is correct.
ADDITIONAL INFORMATION:

• The fundamental frequency of a vibrating string is inversely proportional to its length 
• The frequency is inversely proportional to the square root of the density of the material of the string 
• The frequency is inversely proportional to the square root of the mass of the string 

Beats are the gradual loudening and softening of sound when two sounds waves of similar frequencies interfere constructively or destructively.Hence, the correct answer is D