Wave equation, wavelenght not given

[AncientOne99]

Homework Statement

Wave problem
Given data :
f = 20 Hz
y0 = 0.005 m
t = 0.1 s
x = 0.4 m1. The end portions of stretched string oscillates in the transverse direction with a frequency of 20 Hz and an amplitude of 0.005 m. Wave , which travels along the string, made in 0.1 second, 0.4 m long path.
The speed of each part of string written by the equation v = v0 cos (ωt - kx).
a) What are the constants v0, ω and k to?
b) What is the maximum acceleration of each part of string?
c) What is the distance between the parts of the string, which varies with the phase difference Δ φ = π / 2?
d) How much time does a part of string need to travel from one extreme point to another?

Homework Equations

y(x, t) =y0sin(ωt - kx)
v(x, t)= v0cos (ωt - kx)
c = ƒ λ
ω = 2πf
k = 2π/λ

The Attempt at a Solution

I tried to solve for a wave number but i don't know how to calculate wavelenght.
I don't really well know the diferrence between these three equations for wave.
1. velocity = displacement / time
2. wave velocity = wavelenght / period
3. velocity (particle) = v0 cos (ωt - kx)
1. and 2. equation seem very similar but i don't know if they are really.

 

[ehild]

Homework Statement

Wave problem
Given data :
f = 20 Hz
y0 = 0.005 m
t = 0.1 s
x = 0.4 m1. The end portions of stretched string oscillates in the transverse direction with a frequency of 20 Hz and an amplitude of 0.005 m. Wave , which travels along the string, made in 0.1 second, 0.4 m long path.
The speed of each part of string written by the equation v = v0 cos (ωt - kx).
a) What are the constants v0, ω and k to?
b) What is the maximum acceleration of each part of string?
c) What is the distance between the parts of the string, which varies with the phase difference Δ φ = π / 2?
d) How much time does a part of string need to travel from one extreme point to another?

Homework Equations

y(x, t) =y0sin(ωt - kx)
v(x, t)= v0cos (ωt - kx)
c = ƒ λ
ω = 2πf
k = 2π/λ

The Attempt at a Solution

I tried to solve for a wave number but i don't know how to calculate wavelenght.
I don't really well know the diferrence between these three equations for wave.
1. velocity = displacement / time
2. wave velocity = wavelenght / period
3. velocity (particle) = v0 cos (ωt - kx)
1. and 2. equation seem very similar but i don't know if they are really.

What does this sentence mean?

Wave , which travels along the string, made in 0.1 second, 0.4 m long path.

How do you get the speed of the wave from this information?

 

[AncientOne99]

Speed of wave = displacement of wave / time elapsed
I was thinking about similarity between
velocity of wave and speed of wave so like:

c = 20 Hz * λ
v = 0.1s * 0.4m

And then I equal c and v is the next step.
c=v and from that calculated λ but i don't know if i can do that, i don't have any knowledge about partial derivatives and y(x,t) functions from math.
Any suggestions?

 

[kuruman]

v = 0.1s * 0.4m

Speed is not distance times time. What is it?

 

[AncientOne99]

v = 0.4m/0.1s = 4m/s

 

[kuruman]

v = 0.4m/0.1s = 4m/s

Good. Can you find the wavelength now?

 

[AncientOne99]

Yes i equal two equations.