Explanation 1) Concept: We can find the equation of the wave at x = 0 as given in the graph. From the slope of the graph, we can predict the approximate value of the phase constant. Then, from the expression for acceleration of the given wave at t=0, we can easily get the value of phase constant ϕ . 2) Given: i) Transverse acceleration (a y ) vs t graph at x = 0 ii) Wave equation is y ( x , t ) = y m s i n k x - ω t + ϕ iii) Caution: A calculator does not always give the proper inverse trig function, so check your answer by substituting it and an assumed value of v into y ( x , t ) and then plotting the function. 3) Calculations: The equation of the wave is given as y = y m s i n k x - ω t + ϕ At x = 0, it becomes, y = y m s i n - ω t + ϕ … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … . ( 1 ) At x = 0, acceleration is maximum. Hence, a y = a m = - ω 2 y From equation 1, a y = - ω 2 y s i n - ω t + ϕ This is the equation for the given graph. The slope of the graph is, d a y d t = = d d t - ω 2 y m s i n - ω t + ϕ d y d t = ω 3 y m c o s - ω t + ϕ From the given graph, we can conclude that the slope of the graph at t = 0 is negative

11th Edition

ISBN: 9781119472780

Author: Halliday

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 70P

To determine

To find:

The value of ϕ.

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Chapter 16, Problem 69P

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FUNDAMENTALS OF PHYSICS,AP ED.

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