Ch 16: Sound & Hearing

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경

Young & Freedman Calc 14th Edition

Ch 16: Sound & Hearing

문제 6b

16장, 문제 6b

A metal bar with a length of 1.50 m has density 6400 kg/m³. Longitudinal sound waves take 3.90 × 10^-4 s to travel from one end of the bar to the other. What is Young's modulus for this metal?

검증된 단계별 안내

First, understand that Young's modulus (E) is a measure of the stiffness of a material and is defined as the ratio of stress to strain. In this problem, we can use the relationship between the speed of sound in a material, its density, and Young's modulus.

The speed of sound (v) in a material is given by the formula:

v = \sqrt{\frac{E}{ρ}}

, where

E

is Young's modulus and

ρ

is the density of the material.

Calculate the speed of sound in the metal bar using the formula:

v = \frac{L}{t}

, where

L

is the length of the bar (1.50 m) and

t

is the time taken for the sound to travel (3.90 * 10^-4 s).

Substitute the calculated speed of sound and the given density into the formula for the speed of sound:

v = \sqrt{\frac{E}{ρ}}

. Rearrange this equation to solve for Young's modulus:

E = v^2 ρ

Finally, calculate Young's modulus using the values obtained for the speed of sound and the given density of the metal. This will give you the stiffness of the metal in terms of Young's modulus.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

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

Density

Density is a measure of mass per unit volume, expressed in kg/m³. It is crucial for calculating the speed of sound in a material, as it affects how tightly packed the particles are, influencing how sound waves propagate through the medium.

Speed of Sound in Solids

The speed of sound in a solid is determined by the material's density and its elastic properties, specifically Young's modulus. It is calculated using the formula v = √(E/ρ), where v is the speed of sound, E is Young's modulus, and ρ is the density. This relationship helps in determining how quickly sound waves travel through the material.

Young's Modulus

Young's modulus is a measure of the stiffness of a material, defined as the ratio of stress to strain in the linear elasticity regime of a uniaxial deformation. It is expressed in pascals (Pa) and is essential for understanding how a material deforms under stress, influencing the speed of sound in the material.