Problem: The nodes of a standing wave are points at which the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example, that the point at which a string is tied to a support has zero displacement at all times (i.e., the point of attachment does not move). Consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave: y(x,t) = Asin(kx)sin(ωt), where A is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wavenumber, ω is the angular frequency of the wave, and t is time.Part A:Which one of the following statements about such a wave as described in the problem introduction is correct?A. This wave is traveling in the +x direction.B. This wave is traveling in the x direction.C. This wave is oscillating but not traveling.D. This wave is traveling but not oscillating.Part B:At time t = 0, what is the displacement of the string y(x,0)?Express your answer in terms of A, k, and other previously introduced quantities.

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Part A

For the wave described, each part of the string is oscillating with the same phase. Thus, the wave does not appear to move left or right, but it oscillates up and down.

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Problem Details

The nodes of a standing wave are points at which the displacement of the wave is zero at all times. Nodes are important for matching boundary conditions, for example, that the point at which a string is tied to a support has zero displacement at all times (i.e., the point of attachment does not move). Consider a standing wave, where y represents the transverse displacement of a string that extends along the x direction. Here is a common mathematical form for such a wave: y(x,t) = Asin(kx)sin(ωt), where A is the maximum transverse displacement of the string (the amplitude of the wave), which is assumed to be nonzero, k is the wavenumber, ω is the angular frequency of the wave, and t is time.

Part A:

Which one of the following statements about such a wave as described in the problem introduction is correct?

A. This wave is traveling in the +x direction.

B. This wave is traveling in the x direction.

C. This wave is oscillating but not traveling.

D. This wave is traveling but not oscillating.

Part B:

At time = 0, what is the displacement of the string y(x,0)?

Express your answer in terms of A, k, and other previously introduced quantities.

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