# Wave equation, wavelenght not given

#### AncientOne99

1. The problem statement, all variables and given/known data
Wave problem
Given data :
f = 20 Hz
y0 = 0.005 m
t = 0.1 s
x = 0.4 m

1. 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?
2. Relevant equations
y(x, t) =y0sin(ωt - kx)
v(x, t)= v0cos (ωt - kx)
c = ƒ λ
ω = 2πf
k = 2π/λ
3. 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 equasions 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.

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#### ehild

Homework Helper
1. The problem statement, all variables and given/known data
Wave problem
Given data :
f = 20 Hz
y0 = 0.005 m
t = 0.1 s
x = 0.4 m

1. 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?
2. Relevant equations
y(x, t) =y0sin(ωt - kx)
v(x, t)= v0cos (ωt - kx)
c = ƒ λ
ω = 2πf
k = 2π/λ
3. 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 equasions 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

#### 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?

Science Advisor
Homework Helper
Gold Member

#### AncientOne99

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

Science Advisor
Homework Helper
Gold Member

#### AncientOne99

Yes i equal two equasions.

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