### Question

Why does sound wave travel faster in a denser medium whereas light travels slower?

Sound is a mechanical wave and travels by compression and rarefaction of the medium. Its velocity in an elastic medium is proportional to the square root of Tension in the medium. A higher density leads to more elasticity in the medium and hence the ease by which compression and rarefaction can take place. This way the velocity of sound increases by increase in density.

Light on the other hand is a transverse electromagnetic wave. It does not depend on the elastic property of the medium in which it travels. Its velocity in a medium is determined by the electromagnetic (e.g. dielectric) properties of the medium. Effective path length on the other hand is increased by an increase in the density and hence it leads to higher refractive index and lower velocity.
Answered by: Shandar Ahmad, Ph.D. in Physics, Jamia Millia Islamia, New Delhi

This is is a good question since it forces us to interpret what is meant by a sound wave and a light wave. This may indeed get into complex subject matter, thus I will first give a brief answer followed by explanations.

1)Sound requires a medium in which to travel, such as a gas, liquid, or solid. This is why there can be no sound in outer space since it is a vacuum (i.e. absent of matter). Sound is essentially a pressure wave which causes the medium (i.e. molecules in air) to oscillate, this oscillation is thus propagated through the medium by the matter making it up. Hence we can argue that since a medium is required for sound to propagate, and that the closer the molecules in that medium are to each other the faster the sound will travel.

2)Light does not require a medium (one of the discoveries that mark the beginning of modern physics) in which to propagate. What light is, when we think of it as a wave, is a pair of oscillating electric and magnetic fields which propagate through space. In the absence of matter electromagnetic waves (e.g. light) are free to move at their maximum velocity (~3*10^8 m/s), but when traveling though matter the velocity of light is dependent on the conductivity of the substance. This is actually a very complicated matter, which perhaps is best if we leave it at this: since light becomes dependent on the ability of the molecules making up the substance to move the E-M waves from one point to another the light wave slows down (in relation to its velocity in a vacuum).

Neither answer published corrects the assumption that increased density means increased speed for sound. Actually, increased density DECREASES the speed of sound in a medium.

While increased density can mean increased rigidity, or stiffness, it is not always the case. Greater density can be due to each molecule or atom having more momentum, and being slower to respond to the vibration of its neighbor. The formula for determining the speed of sound in any material shows an INVERSE relationship between velocity and density, but a DIRECT relationship with the material's rigidity.
Answered by: Paul Walorski - A.B. Physics

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