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

Fundamental frequency of the air column is 128 Hz

Step-by-step 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