Nodes the a Standing wave (Sine)
The nodes of a was standing wave space points at wurbanbreathnyc.comch thedisplacement that the wave is zero at all times. Nodes are vital formatcurbanbreathnyc.comng border conditions, for example, the the allude at i beg your pardon astring is tied come a support has actually zero displacement at every times (i.e.,the suggest of attachments does no move).

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Consider a was standing wave, wherein

represents the transverse displacement of a string the extends follow me the x direction. Here is a typical mathematical type for together a wave:

wherein is the best transverse displacement that the string (the amplitude that the wave), i beg your pardon is assumed to be nonzero, is the wave number, is the angular frequency of the wave, and also
is time.
Wurbanbreathnyc.comch one of the following statements around such a tide as described in the problem advent is correct?
Turbanbreathnyc.coms wave is travel in the
direction.Turbanbreathnyc.coms wave is travel in the
direction.Turbanbreathnyc.coms tide is oscillating however not traveling.Turbanbreathnyc.coms tide is traveling but not oscillating.

Eachpart the the cable oscillates through the exact same phase, so the tide does notappear to relocate left or right; rather, that oscillates up and down only.
At time
, what is the displacement the the cable ?
Express your answer in terms of , , and other previously introduced quantities.
What is the displacement the the string together a function of at time
, wherein
is the duration of oscillation the the string?
Part C.1Find the duration in terms of

Part no displayed

Part C.2
 Part not displayed

Express the displacement in regards to , , , and also other constants; the is, advice
and also substitute it in the expression for .

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At wurbanbreathnyc.comch three points
,
, and also
closest come
yet with
0" align="middle"> will certainly the displacement the the wire be zero for every times? These room the very first three nodal points.