Bulk Modulus and the speed of sound

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Materials with a higher bulk modulus allow sound waves to propagate faster due to their resistance to compression. A high bulk modulus indicates that a material requires significantly more pressure to achieve the same volume contraction compared to materials with a lower modulus. This increased resistance means that when a sound wave, which is essentially a pressure wave, travels through the material, it encounters less opposition to its propagation. Consequently, the material's tendency to resist compression facilitates quicker transmission of sound waves. Thus, the relationship between bulk modulus and sound speed is rooted in the material's ability to withstand pressure changes effectively.
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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.
 
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