The de broglie hypothesis suggests a particle can be associated with a wave of momentum $p = \hbar k$
my question is the following: how does one arrive at this concept of the momentum of a wave?
I understand the classical definition of momentum, however I do not see an obvious extension to an object such as a vibrating guitar string.
De Broglie is saying that if I have a vibrating guitar string and the wavelenth of vibration decreases then the momentum of the guitar string increases? Is it the case that a guitar string at a higher frequency(time) has higher energy? is the case that a guitar string vibrating at a higher spatial frequency will also have higher energy? etc.
I'm sorry if this guitar string example is bad... i'm just trying to understand this properly