# The wave of 2 strings

1. Oct 8, 2016

### Hamal_Arietis

1. The problem statement, all variables and given/known data
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 $\frac{L_2-L_1}{L_1}$

2. Relevant equations
The answer is $\frac{L_2-L_1}{L_1}=\frac{n}{n-f_1}$

3. 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 cant 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 .

2. Oct 8, 2016

### Staff: Mentor

Look up "beat frequency".

3. Oct 8, 2016

### Hamal_Arietis

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

4. Oct 8, 2016

### Staff: Mentor

You can take it as given.

5. Oct 8, 2016

### 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 dont use f=f1+f2 ?

6. Oct 8, 2016

7. Oct 8, 2016

Thanks