Question

One of the harmonics of a column of air open at one end and closed at the other 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?

Answer 1

Answer:

Fundamental frequency of the air column is 128 Hz

Explanation:

The general relation to determine the nth- harmonic in column of air is:

$f_{n} =nf_{1}$

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 :

$f_{n} =nf_{1}$       .....(1)

$f_{n+1} =(n+1)f_{1}$      ....(2)

Subtract equation (2) and (1).

$f_{n+1}-f_{n} =f_{1}$

Substitute 576 Hz for $f_{n+1}$ and 448 Hz for $f_{n}$ in the above equation.

(576 - 448 ) Hz = f₁

f₁ = 128 Hz