Calculating Vertical Velocity of Propagating Waves in a String

[susdu]

Homework Statement

Two waves are propagating in a long uniform string of linear mass density μ and tension Fτ.
Their equations are:

y₁=A₁cos(k₁x-w₁t)
y₂=A₂cos(k₂x-w₂t)

Known: λ₁ (wavelength of y1), λ₂, A₁, A₂

what is the vertical velocity of the string at x=2m and t=5s?

Homework Equations

v=sqrt(Fτ/μ)=w/k
k=2π/λ
standard wave equation and solutions

The Attempt at a Solution

just to check I'm on track. what I did was defining:
g(x,t)=y₁+y₂ and finding all the missing varibles (w,k) using formulas.
I then differentiated g with respect to t and plugged x=2,t=5 in the derivative

is this correct?

 

[Dick]

Homework Statement

Two waves are propagating in a long uniform string of linear mass density μ and tension Fτ.
Their equations are:

y₁=A₁cos(k₁x-w₁t)
y₂=A₂cos(k₂x-w₂t)

Known: λ₁ (wavelength of y1), λ₂, A₁, A₂

what is the vertical velocity of the string at x=2m and t=5s?

Homework Equations

v=sqrt(Fτ/μ)=w/k
k=2π/λ
standard wave equation and solutions

The Attempt at a Solution

just to check I'm on track. what I did was defining:
g(x,t)=y₁+y₂ and finding all the missing varibles (w,k) using formulas.
I then differentiated g with respect to t and plugged x=2,t=5 in the derivative

is this correct?

That would be the correct procedure, yes.

 

[susdu]

thanks!