Explanation 1) Concept: We use the concept of wave motion. We can differentiate the given equation for velocity and take the ratio of displacement by velocity. At initial values of x and t, we get the equation for ϕ , plugging the given values, we get the value for phase constant. 2) Formulae: v = d y d t 3) Given: i) Angular frequency is ω = 440 r a d / s ii) Displacement y = + 4.5 m m iii) Transverse velocity is u = - 0.75 m / s iv) Wave equation is y x , t = y m s i n ⁡ ( k x - ω t + ϕ ) 4) Calculations: We know that velocity is u ( x , t ) = d y d t = d y m sin ⁡ k x - ω t + ϕ d t u ( x , t ) = - y m ω c o s ⁡ ( k x - ω t + ϕ ) We know the equation of wave y x , t = y m s i n ⁡ ( k x - ω t + ϕ ) We can take the ratio of y ( x , t ) and u ( x , t ) y x , t u x , t = y m sin ⁡ k x - ω t + ϕ - y m ω cos ⁡ k x - ω t + ϕ y

11th Edition

ISBN: 9781119286240

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: WILEY

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Interference of sound

Seiche

A seiche is an oscillating standing wave in a body of water. The term seiche pronounced saysh) can be understood by the sloshing of water back and forth in a swimming pool. The same phenomenon happens on a much larger scale in vast bodies of water includ…

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Chapter 16, Problem 73P

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Phase constant ϕ

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Chapter 16, Problem 72P

Chapter 16, Problem 74P

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Chapter 16 Solutions

Fundamentals Of Physics

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Phase constant ϕ

Solution Summary: The author explains the concept of wave motion and calculates the phase constant using x and t values.

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Chapter 16 Solutions

To find:

Phase constant ϕ