concerning the effects of temperature and density on the speed of sound [duplicate]

This question already has an answer here:

here is my relatively broad question:
how does the temperature and density of a medium effect the speed at which sound travels through it?

Now I shall elaborate:

it is my understanding that there is some sort of ratio between these two factors that determine the speed of sound in the medium.

from this, I assume that sound travels faster in objects that have a higher temperature (due to atoms/molecules having more energy and hence being more inclined to transfer energy more quickly in order to assume its former energy state and become more stable) and a higher density (which I can only assume to be because the particles are closer together and so somehow travel faster because of this, however, couldn't one also say that the opposite is true because there is less obstruction to block the waves? this is a point of confusion for me, help would be appreciated).

is there some sort of relationship or equation that relates the three factors and are there any other factors that determine the speed of sound in an object (eg. elastic properties of the medium)?

is there a value for this ratio that maximises the speed of sound (ie. some sort of linear constant) and is the relationship between speed and temperature and speed and density linear? if not what is it?

finally, with regard to the equations V=λ/T V=fλ and T=1/f where T=period, is the speed (velocity) of sound also dependent on the frequency and wavelength of the sound waves, or is it the other way round in which the frequency and wavelength are dependant on the velocity of the wave which is in turn dependant on other factors such as temperature and density? of course if the latter is true, what decides how the given product of frequency and wavelength is factored into individual components?