gPhy MasteringPhysics: Assign... x https: n masterin gphys /myct/i signment D-62

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gPhy MasteringPhysics: Assign... x https: n masterin gphys /myct/i signment D-62205864 close Phys 2109-2110 Signed in as Emily Wiedemann Help Assignment 30 em 1 Resources Item 1 The principle of superposition states that if two functions each separately satisfy the wave equation, then the sum (or difference) also satisfies the wave equation. This principle ct th Learning Goal: Part B. These waves have been Consider the sum of two waves yh (2, t ya (z, t here yu (z,t) is the wave described in Part A and y (z,t) is the wave described in chosen so that their sum can be written as follows To see how two traveling waves of the same frequency create a standing wave Consider a traveling wave described by the formula This form is significant because y (z), called the envelope, depends only on position, and yt(t) depend only on time. Traditionally, the time function is taken to be a kar wt trigonometric function with unit amplitude, that is, the overall amplitude of the wave is written as part of ye(z) This function might represent the lateral displacement of a string, a local electric field, the position of the surface of a body of water, or any of a number of other physical manifestations of waves. Part C Find y and yt(t). Keep in mind that yu(t) should be a trigonometric function of unit amplitude. Express your answers in terms of A, k, z, w, and t. Separate the two functions with a comma. ye (z), yt(t) Sub Hints My Answers Give Up Re Part D Which one of the following statements about the superposition wave ys(z, t) is correct? This wave is traveling in the +ac direction This wave is traveling in the -ac direction This wave is oscillating but not traveling This wave is traveling but not oscillating 12:04 PM 4/23/2016

Explanation / Answer

Part C

Find ye(x) and yt(t). Keep in mind that yt(t) should be a trigonometric function of unit amplitude.

Express your answers in terms of A, k, x, ?, and t. Separate the two functions with a comma.

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Part D

Which one of the following statements about the superposition wave ys(x,t) is correct?

Which one of the following statements about the superposition wave  is correct?

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A wave that oscillates in place is called a standing wave. Because each part of the string oscillates with the same phase, the wave does not appear to move left or right; rather, it oscillates up and down only.

Part E

At the position x=0, what is the displacement of the string (assuming that the standing wave ys(x,t) is present)?

Express your answer in terms of parameters given in the problem introduction.

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This could be a useful property of this standing wave, since it could represent a string tied to a post or otherwise constrained at position x=0. Such solutions will be important in treating normal modes that arise when there are two such constraints.

Part F

At certain times, the string will be perfectly straight. Find the first time t1>0 when this is true.

Express t1 in terms of ?, k, and necessary constants.

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ye(x), yt(t) = 2Asin(kx),cos(?t)

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