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What is the speed of sound in a perfectly rigid rod? What is the speed of sound in free space?

Sound is a longitudinal wave and needs a medium to transmit from one location to another. In air, the sound travels by compression and rarefaction of air in the direction of wave motion. In other words, the air molecules move back and forth (which causes compression and decompression of air pockets) in the direction of the sound wave and this causes them to transmit from one location to another. That is, in the simplest terms, sound cannot travel in the absence of a medium.


Thus, in free space (or a vacuum), the speed of sound is zero. This is because there is no medium to transmit the sound wave.


In comparison, in the case of a perfectly rigid rod, there is no free atom or molecule and all the particles move as a single body. Thus, the sound would be transmitted instantly from the rigid body and hence the speed of sound through a rigid body is infinite. Another way to understand this scenario is by mathematical formulation of the speed of sound, which is:


`c = sqrt(E/rho)`


Here, c is speed of sound, E is modulus of elasticity (ratio of stress and strain) and `rho` is density. Since strain is zero for a rigid body (no change in length), E is infinite for a rigid body and so is the speed of sound through it.


Hope this helps. 

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