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

=>    

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

causes

fossil fuels burn

cities become more industrialized

human population grows worldwide