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Chapter 17: Q74P (page 511)

The average density of Earth’s crust 10 kmbeneath the continents is 2.7 g/cm3. The speed of longitudinal seismic waves at that depth, found by timing their arrival from distant earthquakes, is role="math" localid="1661499978175" 5.4 km/s. Use this information to find the bulk modulus of Earth’s crust at that depth. For comparison, the bulk modulus of steel is about role="math" localid="1661499995851" 16×1010 Pa.

Short Answer

Expert verified

Bulk Modulus of earth’s crust at depth is 7.9×1010 Pa.

Step by step solution

01

The given data

  1. Density of earth, ρ=2.7 g/cm3or2.7×103 kg/m3
  2. Speed of longitudinal seismic wave, v=5.4 km/sor5400 m/s
02

Understanding the concept of bulk modulus

Here, we have to use the relation between velocity, the density of the earth, and bulk modulus to find bulk modulus.

Formula:

The velocity of the wave,

v=Bρ …(i)

03

Calculation of bulk modulus of Earth’s crust at depth

Using equation (i) and the given values, we get the value of bulk modulus of Earth’s crust at depth as:

5.4×103 m/s=B2.7×103 kg/m3B=7.87×1010 PaB≃7.9×1010 Pa

Hence, the value of bulk modulus is 7.9×1010 Pa.

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