The two nearest harmonics of a tube closed at one end and open at the other end are $220\text{Hz}$ and $260\text{Hz}$. What is the fundamental frequency of the system?

For a closed organ pipe, only odd harmonics are present ($f,3f,5f,\dots$).The difference between any two successive harmonics is:
$$\Delta f=(2n+1)f-(2n-1)f=2f$$
Given the two nearest harmonics are $220\text{Hz}$ and $260\text{Hz}$:
$$2f=260-220=40\text{Hz}$$
$$f=20\text{Hz}$$
The fundamental frequency is $20\text{Hz}$.