(a) 288 Hz
The difference between any two harmonics of an open-end tube is equal to the fundamental frequency,
(first harmonic):
(1)
In this problem, we are told the frequencies of two successive harmonics:

So the fundamental frequency is:

Now we know that one of the the harmonics is
, so its next highest harmonic will have a frequency of

(b) n=4
The frequency of the nth-harmonic is an integer multiple of the fundamental frequency:
(2)
Since we know
, we can solve (2) to find the number n of this harmonic:

(c) 4445 Hz
For a closed pipe (only one end is open), the situation is a bit different, because only odd harmonics are allowed. This means that the frequency of the nth-harmonic is an odd-integer multiple of the fundamental frequency:
(2)
so, the difference between any two harmonics tube is equal to:
(1)
In this problem, we are told the frequencies of two successive harmonics:

So, according to (1), the fundamental frequency is equal to half of this difference:

Now we know that one of the harmonics is
, so its next highest harmonic will have a frequency of

(d) n=17
We said that the frequency of the nth-harmonic is equal to an odd-integer multiple of the fundamental frequency:
(2)
Since we know
, we can solve (2) to find the number n of this harmonic:
