# Homework Help: Transverse velocity of a standing wave

1. Oct 5, 2014

### jhans11

1. The problem statement, all variables and given/known data
A standing wave pattern on a string is described by y(x, t) = 0.054 sin (9πx)(cos 72πt), 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?

NOTE: I have the answers for A-F, i dont have the answers for g,h,i
2. Relevant equations
cos(wt)=0

3. The attempt at a solution
for the velocity to equal zero, cos(wt) has to equal to pi/2, 3pi/2, and so on

wt= pi/2
72pi(t)=pi/2
t=1/144
and repeat with 3pi/2, 5pi/2
for t values of 3/144 and 5/144

2. Oct 11, 2014

### Greg Bernhardt

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Oct 12, 2014

### ehild

It is not true. When cos(wt)=0 the displacement is zero. Find the expression for the velocity.

ehild