Answer :
Answer:
Fundamental frequency of the air column is 128 Hz
Explanation:
The general relation to determine the nth- harmonic in column of air is:
[tex]f_{n} =nf_{1}[/tex]
Here n is nth harmonic and f₁ is the fundamental frequency of the air column.
According to the problem, there are two consecutive harmonics, one of the order n and other is n+1. Thus, there frequencies are given by :
[tex]f_{n} =nf_{1}[/tex] .....(1)
[tex]f_{n+1} =(n+1)f_{1}[/tex] ....(2)
Subtract equation (2) and (1).
[tex]f_{n+1}-f_{n} =f_{1}[/tex]
Substitute 576 Hz for [tex]f_{n+1}[/tex] and 448 Hz for [tex]f_{n}[/tex] in the above equation.
(576 - 448 ) Hz = f₁
f₁ = 128 Hz