Bulk Modulus and the speed of sound

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coreluccio
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Why is it that materials with a higher bulk modulus value allow for sound waves to propagate through them faster? A material with a high bulk modulus requires a relative greater increase in pressure to contract by the same volume as a material with a lower bulk modulus, and as such sound waves are able to propagate through such a medium faster. Why?
 
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If the material requires more pressure to contract, that means it's fighting the contraction harder. So when a pressure (sound) wave passes through, the material hates being contracted and pushes the wave through, making it pass faster.