What units for the wave function of a string?

[Zouatine]

Homework Statement

unit of wave function

Relevant Equations

Ψ(x,t)=φ(x)*sin(ωt+α)

hello , hope all of you are doing well ,

i have question about the unit of the function of waves of string fixed in both boundary , the function of waves is function of two variables x and t , so it's function describe the displacement in function of place and time ,
Ψ(x,t)=φ(x)*sin(ωt+α)
φ(x): is the shape function
ω= 2πν : the angular frequency ν: is the frequency, Hz
α : initial phase

I'm confusing about the unit of this function , i think the unit must be unit of length ( cm , mm ... ) because from the definition we said it's function describe the displacement , and second think is : sin(ωt+α) doesn't have unit and φ(x) must be unit of length . am i right ?

thank you

 

[BvU]

Short answer: yes.