What Factors Determine the Characteristics of Standing Waves on a String?

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A standing wave pattern on a string is described by y(x, t) = 0.086 sin (8πx)(cos 64πt), where x and y are in meters and t is in seconds. For x ≥ 0, what is the location of the node with the (a) smallest, (b) second smallest, and (c) third smallest value of x? (d) What is the period of the oscillatory motion of any (nonnode) point? What are the (e) speed and (f) amplitude of the two traveling waves that interfere to produce this wave? For t ≥ 0, what are the (g) first, (h) second, and (i) third time that all points on the string have zero transverse velocity?


Please provide a solution rather than just an answer :) I really appreciate any help!
 
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A node occurs where there is no net movement of the string. What values of x will make y = 0?
 

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