One of the harmonics of a column of air in a tube that is open at both ends has a frequency of 448 Hz, and the next higher harmonic has a frequency of 576 Hz. What is the fundamental frequency of the air column in this tube?

The fundamental frequency is  

Explanation:

From the question we are told that

   The frequency of one harmonics is  

    The next higher harmonic is  

Generally the frequency of an air column open at both ends is mathematically represented as

Here n  is the order of the harmonics (frequency)

        v is the velocity of the sound

        L  is the length of the column

So for one harmonics we have that

Then for the next higher harmonics

Generally the difference between these frequencies is mathematically represented as  

=>    

=>    

Generally for fundamental  frequency n =  1

So  

So

=>