Trasverse wave wavelenght and velocity problem

[mmoadi]

Homework Statement

Along a long tense rope are traveling transverse waves with amplitude A= 10 cm. What is the wavelength, if at any given time the distance between two consecutive neighboring waves y= 5 cm is d= 6 cm? With what velocity are the waves spreading, if the maximum transverse speed of the rope is ω= 0.1m/s?

Homework Equations

v= fλ
k= 2π/ λ
y= A sin(k*x)

The Attempt at a Solution

For the wavelength:
k= 2π/ λ → λ= 2π/ k

Calculating k:
y= A(sin k)(sin x) → sin k= y/ A(sin x)
sin k= 5, which is wrong

Where is my mistake?

 

[ideasrule]

I don't understand what you did, but the equation for a wave is y=Asin(wt). (Note that the w here is different from the w in the question.) Derive that with respect to t and you get dy/dt=Awcos(wt), so Aw is the rope's maximum transverse speed. From there you can get the frequency, which you can then multiply by the wavelength to get speed.