Answer
4.3 m, and it is an open pipe.
Work Step by Step
We are told that the difference in frequency for two successive harmonics is 320Hz – 280Hz = 40Hz.
Consider a closed pipe. Two successive harmonics differ in frequency by twice the fundamental, so if the pipe is closed, the fundamental is 20 Hz, However, since the harmonics of a closed pipe are odd multiples of the fundamental, this case won’t work, because 280 Hz and 320 Hz are even-numbered multiples of 20 Hz.
Now consider an open pipe. Two successive harmonics differ in frequency by the fundamental, so if the pipe is open, the fundamental is 40 Hz, (The given frequencies would be 7th and 8th harmonics, respectively.) Aha!
The fundamental frequency is $f_1=\frac{v}{2 \mathcal{l}}$.
At the given temperature, find the length, using the speed of sound (formula on page 329).
$$\mathcal{l}=\frac{v}{2f_1}=\frac{331+(0.60)(23.0)}{2(40Hz)}=4.3m $$
