Answer
The harmonic frequency $840~Hz$ is the fourth harmonic.
Work Step by Step
We can write an expression for the harmonic frequencies of a tube with one open end:
$f = \frac{nv}{4L},~~$ where $~~n = 1,3,5,...$
Note that the difference between each successive harmonic frequency is $2f_1$ where $f_1$ is the fundamental frequency.
We can find the difference in the frequency of successive harmonics:
$\Delta f = 1320~Hz-1080~Hz = 240~Hz$
then $f_1 = \frac{240~Hz}{2} = 120~Hz$
We can find the next highest harmonic frequency after $600~Hz$:
$f = 600~Hz+240~Hz = 840~Hz$
We can list the harmonic frequencies of this tube:
$f = 120~Hz, 360~Hz, 600~Hz, 840~Hz, 1080~Hz, 1320~Hz, ...$
The harmonic frequency $840~Hz$ is the fourth harmonic.
