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Ch 15: Mechanical Waves
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
All textbooksYoung & Freedman Calc 14th EditionCh 15: Mechanical WavesProblem 29
Chapter 15, Problem 29

At a distance of 7.00 x 1012 m from a star, the intensity of the radiation from the star is 15.4 W/m2. Assuming that the star radiates uniformly in all directions, what is the total power output of the star?

Verified step by step guidance
1
Understand that the intensity (I) of radiation is defined as the power (P) per unit area (A), given by the formula: I = P / A.
Recognize that the area (A) over which the star's radiation is spread is the surface area of a sphere with radius equal to the distance from the star, which is 7.00x10^12 m. The formula for the surface area of a sphere is A = 4πr^2.
Substitute the given distance into the surface area formula: A = 4π(7.00x10^12 m)^2.
Rearrange the intensity formula to solve for the total power output (P) of the star: P = I * A.
Substitute the given intensity (15.4 W/m^2) and the calculated area into the formula to find the total power output: P = 15.4 W/m^2 * 4π(7.00x10^12 m)^2.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Intensity of Radiation

Intensity is the power per unit area received from a source, measured in watts per square meter (W/m^2). It describes how much energy is received by a surface at a given distance from the source. In this problem, the intensity is given as 15.4 W/m^2 at a distance of 7.00x10^12 meters from the star.
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Inverse Square Law

The inverse square law states that the intensity of radiation from a point source decreases with the square of the distance from the source. Mathematically, it is expressed as I = P / (4πr^2), where I is the intensity, P is the power output, and r is the distance from the source. This principle is crucial for calculating the total power output of the star.
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Total Power Output

Total power output, or luminosity, is the total amount of energy emitted by a star per unit time, measured in watts (W). It can be calculated using the formula P = I * 4πr^2, where I is the intensity at a given distance, and r is the distance from the star. This formula allows us to determine the star's total energy emission based on the observed intensity at a specific distance.
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Related Practice
Textbook Question

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.

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Textbook Question

Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm.

<Image>

Sketch the shape of the string at the end of 6.0 s.

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Textbook Question

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;

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Textbook Question

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.

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Textbook Question

Two pulses are moving in opposite directions at 1.0 cm/s on a taut string, as shown in Fig. E15.34. Each square is 1.0 cm. <IMAGE> Sketch the shape of the string at the end of 7.0 s.

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Textbook Question

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?

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