The two nearest harmonics of a tube closed at one end and open at other end are 220 Hz and 260 Hz. What is the fundamental frequency of the system?

Concept:

A harmonic is a wave with a frequency that is a positive integral multiple of the frequency of the wave called as the fundamental frequency.

The original wave is also called the first harmonic and the following harmonics of  first harmonic are called as higher harmonics.

Formula to calculate nth harmonic of the tube is:

\(\rm\frac{(2n+1)v}{4l}\)

Calculation:

Two successive frequencies of closed pipe

\(\rm\frac{nv}{4l} = 220\)    ---(i)

\(\frac{(n+2)V}{4I} =260\)     ---(ii)

Divinding (ii) by (i), we get

\(\frac{n+2}{n}=\frac{260}{220}=\frac{13}{11}\)

11n + 22 = 13n

n = 11

So, \(\rm11\frac{V}{4l}=220\)

\(\rm\frac{v}{4l}=20\)

So fundamental frequency is 20 Hz.