Resonance in String: Understanding Wave Interference According to Book

[AdityaDev]

according to book "...Let us look at a particular wave crest generated at the left end of the string by a fork. It travels to the right end of the string, is reflected back, and is reflected again at the fork.Now it interferes with the next wave..."
doubt: the fork keeps vibrating and keeps producing waves. so just after it is reflected from the right end, it will interfere with the next crest right? why didthe author assume the first crest traveled 2L distance without interference? wouldn't it interfere withe next frest just after it travels a distance L?

 

[Simon Bridge]

The author is presenting a simplified picture. You should realize that all parts of the "incoming wave" interfere with all parts of the "reflected wave" to produce the wave you actually see.

The setup described is both driven and damped - but you don't have the maths for that yet.

 

[AdityaDev]

The author is presenting a simplified picture. You should realize that all parts of the "incoming wave" interfere with all parts of the "reflected wave" to produce the wave you actually see.

The setup described is both driven and damped - but you don't have the maths for that yet.

So the formula $f=\frac{n}{2l}\sqrt{\frac{T}{\mu}}$ is wrong?

 

[Simon Bridge]

Wrong for what purpose?
Context is everything.