Calculate the speed of longitudinal waves in granite, using Tables in Chapters 12 and 13.

검증된 단계별 안내

Identify the formula for the speed of longitudinal waves (sound waves) in a solid material. The formula is:

v = \sqrt{\frac{K}{ρ}}

, where

K

is the bulk modulus of the material and

ρ

is the density of the material.

Refer to the tables in Chapters 12 and 13 to find the bulk modulus (

K

) and density (

ρ

) of granite. For example, the bulk modulus of granite might be approximately

4.5 \times 10^{10} Pa

, and its density might be around

2700 kg / m^{3}

Substitute the values of

K

and

ρ

into the formula. For example:

v = \sqrt{\frac{4.5}{\times}}

Simplify the expression under the square root to calculate the ratio of the bulk modulus to the density. This step involves dividing the bulk modulus by the density.

Take the square root of the result from the previous step to find the speed of longitudinal waves in granite. Ensure the units are consistent, and the final speed is expressed in meters per second (m/s).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Longitudinal Waves

Longitudinal waves are waves in which the particle displacement is parallel to the direction of wave propagation. In these waves, compressions and rarefactions move through the medium, allowing energy to transfer without the bulk movement of matter. Sound waves in air and seismic P-waves are common examples of longitudinal waves.

Wave Speed Calculation

The speed of a wave is determined by the properties of the medium through which it travels. For longitudinal waves, the speed can be calculated using the formula v = √(E/ρ), where E is the modulus of elasticity (or bulk modulus) and ρ is the density of the material. This relationship highlights how both the stiffness and density of a medium influence wave speed.

Material Properties of Granite

Granite is an igneous rock composed mainly of quartz, feldspar, and mica, characterized by its density and elasticity. The specific values for the bulk modulus and density of granite are essential for calculating the speed of longitudinal waves in this material. Understanding these properties allows for accurate predictions of wave behavior in geological contexts.