What is the ratio of lengths for two vibrating strings with a beat frequency?

[Hamal_Arietis]

Homework Statement

Two strings are stretched tautly parallel to each other. The length of one is L1 and the length of the other is L2(>L1). When both are simultaneously made to undergo fundamental vibration, beats can be heard at a frequency n. The waves in both strings travel at the same speed. Let us denote the fundamental freqency of the string with length L1 as f1.
Find the ratio $\frac{L_2-L_1}{L_1}$

Homework Equations

The answer is $\frac{L_2-L_1}{L_1}=\frac{n}{n-f_1}$

The Attempt at a Solution

I have some equation about wave in two strings:
$L_1=\frac{v}{2f_1}$
And
$L_1=i_1\frac{v}{2n};L_2=i_2\frac{v}{2n}$
But I can't solve as answer.
And What does
"When both are simultaneously made to undergo fundamental vibration, beats can be heard at a frequency n" mean?
Thanks for helping .

 

[gneill]

Look up "beat frequency".

 

[Hamal_Arietis]

The beat frequency means F=|f1-f2| but it is definition or must prove?

 

[gneill]

The beat frequency means F=|f1-f2| but it is definition or must prove?

You can take it as given.

 

[Hamal_Arietis]

I want to prove this equation:
If we have 2 wave: $y=Acos(2\pi f_1t)$ and $y'=Acos(2\pi f_2t)$
We have
$$x=y+y'=2A(cos(\pi (f_1- f_2)t)cos(\pi (f_1+f_2)t)$$
But why we don't use f=f1+f2 ?

 

[gneill]

Take a look at this Hyperphysics entry on beats.

 

[Hamal_Arietis]

Thanks