Ch. 15 - Wave Motion

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 15 - Wave Motion

문제 16

15장, 문제 16

Two earthquake waves of the same frequency travel through the same portion of the Earth, but one is carrying 3.5 times the energy. What is the ratio of the amplitudes of the two waves?

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Understand the relationship between the energy of a wave and its amplitude. The energy of a wave is proportional to the square of its amplitude. Mathematically, this can be expressed as:

E \(\propto\) A^2

, where

E

is the energy and

A

is the amplitude.

Set up the ratio of the energies of the two waves. Let the energy of the first wave be

E_1

and the energy of the second wave be

E_2

. According to the problem,

E_2 = 3.5 \(\cdot\) E_1

Express the relationship between the amplitudes of the two waves using the proportionality:

\(\frac{E_2}{E_1}\) = \(\left\)(\(\frac{A_2}{A_1}\)\(\right\))^2

. Substitute

E_2 = 3.5 \(\cdot\) E_1

into this equation.

Simplify the equation to solve for the ratio of the amplitudes:

\(\frac{A_2}{A_1}\) = \(\sqrt{\frac{E_2}{E_1}\)}

. Substitute

\(\frac{E_2}{E_1}\) = 3.5

into the equation.

Conclude that the ratio of the amplitudes is the square root of 3.5. This gives the final expression:

\(\frac{A_2}{A_1}\) = \(\sqrt{3.5}\)

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주요 개념

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

Energy and Amplitude Relationship

In wave physics, the energy carried by a wave is proportional to the square of its amplitude. This means that if one wave carries more energy than another, we can determine the ratio of their amplitudes by taking the square root of the ratio of their energies.

Wave Properties

Waves are characterized by properties such as frequency, wavelength, and amplitude. Frequency refers to how many cycles occur in a given time, while amplitude measures the maximum displacement from the rest position. Understanding these properties is essential for analyzing wave behavior.

Ratio Calculation

Calculating ratios involves comparing two quantities to understand their relative sizes. In this context, we will use the relationship between energy and amplitude to find the ratio of the amplitudes of the two earthquake waves based on their energy difference.