Question

How many harmonics in the audible range are present in the vibrations of air column in a closed organ pipe of length 0.2m. Given velocity of sound $=340m{s}^{-1}$

• A. 12
• B. 18
• C. 24
• D. 30

Answer 1

The correct option is C 24

$=f=\frac{v}{4l}=\frac{340}{4\times 0.2}=\frac{340}{0.8}=425H_Z$
This is in the audible range. (20 Hz to 20000 Hz)
The next overtones are 3f, 5f . . . . which are present in the pipe
Let there be n harmonics
$nf\le 20000$
$n\le \frac{20000}{425}=47$
The $n^{th}$harmonic present in the pipe is 19975. So the harmonics are 425, 1275, . . . . 19975
Number of terms in this A.P
$19975=425+(n-1)850=425+850n-85019975+425=850n400=850n\therefore n=\frac{20400}{850}=24$

Ans: 24