Beats from Different String Lengths

[rpp293]

Homework Statement

Two strings which are fixed at both ends are identical except that one is 0.57 cm longer than the other. Waves on both of these string propagate with a speed of 34.9 m/sec and the fundamental frequency of the shorter string is 226 Hz.

a) What is frequency of the beat that would result if these two strings were plucked at the same time?

c) What is the beat frequency if the length difference is now 0.72cm?

Homework Equations

f1 =v/2L
fn= n*(v/2L)
fbeat= abs f 1- f 2

The Attempt at a Solution

So I tried using the first equation with f1 being 226Hz and then used the velocity given to solve for the first length. Which I found to be 0.0772123m. Then I subtracted .57cm from that to get length 2 (0.0829123) and used the same equation again except it will now be f2= 2* (34.9/2*0.0829123). This gave me the second freqeuncy of 420.9262362. When I subtract this from 226, it gives me the wrong answer for f beat.
Please advise me as I am not sure at what I am doing wrong at this point. Thanks in advance

 

[zorro]

Hi rpp293!
Welcome to PF!

Then I subtracted .57cm from that to get length 2 (0.0829123) and used the same equation again...

You have to add (not subtract) 0.0057 m to 0.077 m to get the length of the longer string.