Question

A pipe's lower end is immersed in water such that the length of air column from the top open end has a certain length $25cm$. The speed of sound in air is $350m/s$. The air column is found to resonate with a tuning fork of frequency $1750Hz$. By what minimum distance should the pipe be raised in order to make the air column resonate again with the same tuning fork?

• A. $7cm$
• B. $5cm$
• C. $35cm$
• D. $10cm$

Answer 1

Answer: (D)

$10cm$

Given: speed of sound in air, $v=350m/s$

For one sided closed pipe:

Frequency, ${\nu }_n=\frac{(2n-1)v}{4L}$ where $n=1,2,3......$

When length of the pipe is $25cm$ OR $0.25m$, $1750=\frac{(2n-1)350}{4\times 0.25}$

$⟹n=3$

Now let the length of the pipe after raising be $Lm$.

For minimum increase in length of air column, $n=3+1=4$

$⟹1750=\frac{(2\times 4-1)350}{4\times L}$ gives $L=0.35m$

Thus the distance by which the pipe is raised $=0.35-0.25=0.1m=10cm$