Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of $λ_{o} = 589 nm$ . Wavelength $λ$ is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift $λ - λ_{o}$ ?

The wavelength shift for sodium light source is 2.97 nm.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Identification of given data

The proper wavelength of emitting light is $λ_{o} = 589 nm$

The speed of sodium light source is $u = 0.1 c$

The wavelength shift is the variation in the wavelength of light due to relative movement of source and observer in different frames. It is calculated by the wavelength shift formula.

Step 2: Determination of wavelength shift for sodium light source

The wavelength shift for sodium light source is given as:

$λ - λ_{o} = λ_{o} (\frac{1}{\sqrt{1 - {(\frac{v}{c})}^{2}}} - 1)$

Substitute all the values in the above equation.

$λ - λ_{o} = (589 nm) (\frac{1}{\sqrt{1 - {(\frac{0.1 c}{c})}^{2}}} - 1) λ - λ_{o} = 2.97 nm$

Therefore, the wavelength shift for sodium light source is 2.97 nm.

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Fundamentals Of Physics

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Short Answer

A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of $λ_{o} = 589 nm$ . Wavelength $λ$ is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift $λ - λ_{o}$ ?

Step by Step Solution

Step 1: Identification of given data

Step 2: Determination of wavelength shift for sodium light source

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Short Answer

A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of λo=589 nm. Wavelength λ is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift λ-λo?

Step by Step Solution

Step 1: Identification of given data

Step 2: Determination of wavelength shift for sodium light source

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A sodium light source moves in a horizontal circle at a constant speed of 0.100c while emitting light at the proper wavelength of $λ_{o} = 589 nm$ . Wavelength $λ$ is measured for that light by a detector fixed at the center of the circle. What is the wavelength shift $λ - λ_{o}$ ?