Question

The number of possible natural oscillations of air column in a pipe closed at one end of length $85\text{cm}$ whose frequencies lie below $1250\text{Hz}$ are: (Velocity of sound $=340{\text{ms}}^{-1}$)

• A. $4$
• B. $5$
• C. $7$
• D. $6$

Answer 1

The correct option is D $6$

For pipe closed at one end
$f=(2n+1)\frac{v}{4L}$
For $n=0,$ $f_0=\frac{v}{4L}=\frac{340}{4\times 85\times {10}^{-2}}=100\text{Hz}$
Therefore
$n=0,f_0=100\text{Hz}$
$n=1,f_1=3f_0=300\text{Hz}$
$n=2,f_2=5f_0=500\text{Hz}$
$n=3,f_3=7f_0=700\text{Hz}$
$n=4,f_4=9f_0=900\text{Hz}$
$n=5,f_5=11f_0=1100\text{Hz}$
Which are less than $1250\text{Hz}$