Skip to main content
Ch 15: Mechanical Waves
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552당신이 사용하는 게 아니라요?교과서 변경
15장, 문제 27a

Energy Output. By measurement you determine that sound waves are spreading out equally in all directions from a point source and that the intensity is 0.026 W/m2 at a distance of 4.3 m from the source. What is the intensity at a distance of 3.1 m from the source?

검증된 단계별 안내
1
Understand that intensity (I) of a sound wave is defined as the power (P) per unit area (A), and it decreases with distance from the source. The formula for intensity is I = P/A.
Recognize that for a point source emitting sound waves equally in all directions, the area (A) over which the sound spreads is the surface area of a sphere, given by A = 4πr², where r is the distance from the source.
Use the inverse square law for intensity, which states that intensity is inversely proportional to the square of the distance from the source: I₁/I₂ = (r₂/r₁)².
Substitute the known values into the inverse square law formula: I₁ = 0.026 W/m² at r₁ = 4.3 m, and find I₂ at r₂ = 3.1 m.
Solve for I₂ using the formula I₂ = I₁ * (r₁/r₂)², substituting the values to find the intensity at 3.1 m from the source.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
2m
도움이 되었나요?

주요 개념

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

Intensity of Sound Waves

Intensity is the power per unit area carried by a wave, measured in watts per square meter (W/m^2). It describes how much energy a sound wave transmits through a given area and decreases as the distance from the source increases due to the spreading of the wave.
추천 영상:
가이드 코스
04:25
Sound Intensity Level and the Decibel Scale

Inverse Square Law

The inverse square law states that the intensity of a wave is inversely proportional to the square of the distance from the source. This means that as you move further from the source, the intensity decreases rapidly, specifically by a factor of the distance squared.
추천 영상:
가이드 코스
05:26
The Inverse-Square Law for Intensity

Point Source of Sound

A point source is an idealized source of sound that emits waves equally in all directions. This simplification allows for easier calculations of wave properties like intensity, as it assumes uniform distribution of energy across a spherical surface centered on the source.
추천 영상:
가이드 코스
04:25
Sound Intensity Level and the Decibel Scale
관련 실천
교과서 질문

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=(2.30mm)cos[(16.98 rad/m)x+(742 rad/s)t]y(x,t)=\(\left\)(2.30\(\operatorname{mm)}\]\cos\)[\(\left\)(16.98\(\text{ }\)rad/m\(\right\))x+(742\(\text{ }\)rad/s\(\right\))t]. Being more practical, you measure the rope to have a length of 1.35 m1.35\(\text{ m}\) and a mass of 0.00338kg0.00338\(\operatorname{kg}\). You are then asked to determine the following: (f) tension in the rope; (g) average power transmitted by the wave.

1591
views
교과서 질문

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=(2.30mm)cos[(16.98 rad/m)x+(742 rad/s)t]y(x,t)=\(\left\)(2.30\(\operatorname{mm)}\]\cos\)[\(\left\)(16.98\(\text{ }\)rad/m\(\right\))x+(742\(\text{ }\)rad/s\(\right\))t]. Being more practical, you measure the rope to have a length of 1.35 m1.35\(\text{ m}\) and a mass of 0.00338kg0.00338\(\operatorname{kg}\). You are then asked to determine the following: (d) wave speed; (e) direction the wave is traveling;

1586
views
교과서 질문

A fellow student with a mathematical bent tells you that the wave function of a traveling wave on a thin rope is y(x,t)=(2.30mm)cos[(16.98 rad/m)x+(742 rad/s)t]y(x,t)=\(\left\)(2.30\(\operatorname{mm)}\]\cos\)[\(\left\)(16.98\(\text{ }\)rad/m\(\right\))x+(742\(\text{ }\)rad/s\(\right\))t]. Being more practical, you measure the rope to have a length of 1.35 m1.35\(\text{ m}\) and a mass of 0.00338kg0.00338\(\operatorname{kg}\). You are then asked to determine the following: (a) amplitude; (b) frequency; (c) wavelength.

1975
views
교과서 질문

A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the second overtone?

1703
views
교과서 질문

A 1.50-m-long rope is stretched between two supports with a tension that makes the speed of transverse waves 62.0 m/s.What are the wavelength and frequency of the fundamental?

1863
views
교과서 질문

Energy Output. By measurement you determine that sound waves are spreading out equally in all directions from a point source and that the intensity is 0.026 W/m2 at a distance of 4.3 m from the source. How much sound energy does the source emit in one hour if its power output remains constant?

1615
views
1
rank