How Do Sinusoidal Waves Affect String Motion?

[tj.]

Homework Statement

A continuous succession of sinusoidal wave pulses are produced at one end of a very long string and travel along the length of the string. The wave has frequency 36.0Hz, amplitude 5.50mm, and wavelength 0.635m.
a) How long does it take the wave to travel a distance of 8.50m along the length of the string?
b) How long does it take a point on the string to travel a total accumulated transverse distance of 8.50m, once the wave train has reached the point and set it into motion?

Homework Equations

So I've been able to do part a) with ease but the trouble I'm having is with part b). It just completely confuses me!

Do I need to use the equation $y(x,t) = Acos(kx - \omega t)$ or $\frac{\partial^{2}y(x,t)}{\partial x ^{2}} = \frac{1}{v^{2}} \frac{\partial ^{2}y(x,t)}{\partial t^{2}}$ or $v_{y}(x,t) = \omega Asin(kx - \omega t)$ or something different??

The Attempt at a Solution

So for part a) I got t=0.372 seconds using $v=f\lambda$ and b) is an unknown to me.

Thanks in advance if anyone can help!

 

[kuruman]

First find how much distance the point travels in one oscillation, then find how many oscillations correspond to 8.50 m.

 

[tj.]

So I got the exact same answer as part a). Would that be correct??

 

[Redbelly98]

Moderator's note: thread moved to Introductory Physics, as this appears to be college sophomore level physics.

So I got the exact same answer as part a). Would that be correct??

Uh, no. First answer this: how much transverse distance does the point travel in one oscillation? Hint: it is related to the amplitude.

(Back to you, kuruman ... )