I am not a scientist but I have a question about speed of sound in vacuum. All I know is that the speed of sound $v$ in a medium is given by formula $$v= \sqrt{\frac E\rho},$$ where $E$ is elasticity and $\rho$ is density.
And according to a scientist, vacuum is a medium which has elasticity highest comparison to other and it's density is so less it is nearer to zero. Then, from above, the value of velocity of sound in vacuum should be the greatest among all other medium? Am I wrong?
Yes, you're wrong.
Sound waves are small compressions (oscillations) of an elastic medium, travelling through that same elastic medium (as a wave). Air, liquids or solids are typical elastic media through which sound waves can travel.
Vacuum however contains no matter and cannot sustain sound waves at all.
Sound wave is a longitudinal elastic wave which strictly demands the presence of a material medium for its propagation from one place to another. So sound cannot propagate in vacuum (which actually has no mass and thereby no density), leave alone the speed of sound in vacuum.
Moreover, if we consider the definition of elasticity, I think this concept does not really apply to vacuum. Also, for the highest speed of sound, it depends on several external factors like temperature, humidity, material medium of propagation etc. For more information regarding this, you can check the following link.
Sound need a medium to travel or to propagate. In Vacuum no medium will present. So, I think velocity of sound in vacuum is zero 000.
Because the vacuum is not literally "empty" in most models that get down into it, one can make toy models in which pressure/sound waves can propagate, with some niftiness that can emerge given a bit of speculating. A now-very-old paper that makes for easy grad school reading is Stevenson 2002.
For a fluid the elasticity (E) is largely determined by the bulk modulus of elasticity.
If we start with cube of gas with a volume of unity and pressure of unity, then doubling the volume halves the elasticity and also halves the density, so the speed of sound through the medium remains constant as the pressure is reduced. At the point that the density goes to zero, the elasticity also goes to zero, so the speed of sound in a vacuum is not infinite, but is indeterminate. Since sound is normally carried by matter or a medium, there is no reasonable way to define the speed of sound in a vacuum as there is no matter or medium or sound. Reducing the pressure of the gas shows no signs of the speed of sound increasing as the pressure goes to zero.
