Calculating Tune Adjustment for Flutist's Note A: Aa Flutist in 342 m/s Room

[sam.]

1. Homework Statement

Aa flutists assembles her flute in a room where the speed of sound is 342 m/s. When she plays the note A, it is in perfect tune with a 440 Hz tuning fork. After a few minutes, the air inside her flute has warmed to where the speed of sound is 346 m/s.
A) How many beats per second will she hear if she now plays the note A as the tuning fork is sounded?
B) How far does she need to extend the "tuning joint" of her flute to be in tune with the tuning fork?

2. Homework Equations

For an open-open tube:

_m = 2L/m
f_m = mv/2L

3. The Attempt at a Solution

I found the answer for A to be 5 beats/second, but I can't seem to figure out how to calculate B. I tried subbing in f = 440 Hz and v = 346 m/s into the second equation with m=1 but it wasn't the right answer. I know the answer is 4.6 mm but I don't know how they get that. Any help is appreciated!

 

[Dick]

What's the difference in wavelength between a 440Hz wave at v=342m/sec and one at 346m/sec? How does this relate to having an open ended tube? Oh, and don't double post.