Answer
$L = 2.62~m$
Work Step by Step
We can find the frequency of the shorter pipe as:
$f = \frac{v}{2L}$
$f = \frac{343~m/s}{(2)(2.40~m)}$
$f = 71.46~Hz$
Since the beat frequency is 6.0 Hz, the difference between the two frequencies must be 6.0 Hz. Since the longer pipe has a lower frequency, the frequency of the longer pipe is 65.46 Hz. We can find the length of the longer pipe as:
$f = \frac{v}{2L}$
$L = \frac{v}{2f}$
$L = \frac{343~m/s}{(2)(65.46~Hz)}$
$L = 2.62~m$