Two solid rods have the same bulk modulus but one is 2.5 times as dense as the other. In which r

step 1 The speed of a longitudinal wave in solid is given by v is equal to bulk modulus divided by dens

Two solid rods have the same bulk modulus but one is 2.5...

Key Concepts

Density

Density is defined as mass per unit volume and represents the inertia of a material. In the context of wave propagation, a higher density means a greater inertia, which tends to slow down the wave speed since the material resists acceleration. Therefore, when comparing two materials with the same elastic properties, the one with a lower density will generally support faster wave propagation.

Bulk Modulus

The bulk modulus is a measure of a material's resistance to uniform compression. It relates the change in pressure to the relative change in volume when the material is subjected to external forces. In wave propagation contexts, a higher bulk modulus generally implies that the medium is more resistant to compressive deformation, which can affect the speed at which compressional waves travel through the material.

Speed of Longitudinal Waves in Solids

The speed of longitudinal waves in a solid medium depends on both the material’s stiffness (characterized by properties like the bulk modulus) and its density. The relationship is typically given by the square root of the ratio of the modulus to the density. When comparing two rods with the same bulk modulus, the rod with the lower density will exhibit faster wave speeds. If one rod is 2.5 times as dense as the other, the wave in the less dense rod will travel approximately ?2.5 times faster.

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