Answer to Question #77424 in Mechanics | Relativity for Rachael Briggs

Question

I'm doing revision currently and I'm stuck on a question:
A guitar string has its effective length shortened by one third when the players finger presses it against one of the frets. Calculate by what ratio the frequency will be increased.

Apparently the answer is 1.5 times higher frequency but I don't understand how to get to that answer. Can you help me?

Answer 1

f=(v·n)/(2·l)
l_(effective length shortened )=2/3 l
f_(effective length shortened)=(v·n)/(2·2/3 l)=(1.5·v·n)/(2·l)
f_(effective length shortened)=1.5·f
The frequency will increase by 1.5 times