Calculating Beats and Extension for a Flutist in Perfect Tune - Flute Homework"

[sam.]

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?

Homework Equations

For an open-open tube:

\lambda_m = 2L/m
f_m = mv/2L

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!

 

[Gokul43201]

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?

Homework Equations

For an open-open tube:

\lambda_m = 2L/m
f_m = mv/2L

The Attempt at a Solution

I found the answer for A to be 5 beats/second,

This is correct.

...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.

That will give you the length required to produce the correct A note at the higher temperature. You are asked for the extension, which is the difference between the lengths at the high temperature and the low temperature.