A jet plane at takeoff can produce sound of intensity 10.0 W/m² at 30.0 m away. But you prefer the tranquil sound of normal conversation, which is 1.0 μW/m². Assume that the plane behaves like a point source of sound. (a) What is the closest dis-tance you should live from the airport runway to preserve your peace of mind? (b) What intensity from the jet does your friend experience if she lives twice as far from the runway as you do? (c) What power of sound does the jet produce at takeoff?

검증된 단계별 안내

Step 1: Understand the concept of sound intensity and how it relates to distance from a point source. The intensity of sound from a point source decreases with the square of the distance from the source. This is known as the inverse square law for sound intensity.

Step 2: Use the inverse square law to find the closest distance you should live from the airport runway. The formula for sound intensity is I = P / (4πr²), where I is the intensity, P is the power of the source, and r is the distance from the source. You need to solve for r when I is 1.0 μW/m².

Step 3: Calculate the intensity your friend experiences if she lives twice as far from the runway as you do. Use the inverse square law again, knowing that if the distance is doubled, the intensity will be reduced by a factor of four.

Step 4: Determine the power of sound the jet produces at takeoff. Use the given intensity at 30.0 m (10.0 W/m²) and the formula I = P / (4πr²) to solve for P, the power of the sound source.

Step 5: Review the calculations and ensure that the units are consistent throughout the problem. Make sure to convert units where necessary, such as converting μW to W for consistency in calculations.

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주요 개념

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

Sound Intensity

Sound intensity is the power per unit area carried by a sound wave, measured in watts per square meter (W/m^2). It quantifies how much sound energy passes through a given area and is crucial for understanding the loudness of sound at different distances from the source.

Inverse Square Law

The inverse square law states that the intensity of sound from a point source decreases with the square of the distance from the source. This means that as you move away from the sound source, the intensity diminishes rapidly, which is essential for calculating sound levels at various distances.

Sound Power

Sound power is the total energy emitted by a sound source per unit time, measured in watts (W). Unlike intensity, sound power is independent of distance and describes the source's ability to produce sound, which is vital for determining the total acoustic output of the jet plane.

관련 실천

교과서 질문

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교과서 질문

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교과서 질문

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교과서 질문

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