Through which of the following materials do sound waves travel the fastest? air metal vacuum water

The correct answer is Metal.

Sound waves are vibrations which need medium to propagate. Higher the density of medium, the sound travels fastest. Sound travels fastest in solid than liquid and gas. Therefore, in this question sound will travel faster in metal because metal has higher density than air and water and it will not travel in vacuum as sound needs medium to travel.  

The correct answer would be metal because of the higher density of the medium

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