Question

In a resonance column experiment, a tuning fork of frequency $400\text{Hz}$ is used. The first resonance is observed when the air column has a length $20.0\text{cm}$ and the second resonance is observed when the air column has a length of $62.0\text{cm}$. Find the distance above the open end where the pressure node is formed ?

• A. $1.5\text{cm}$
• B. $3\text{cm}$
• C. $2\text{cm}$
• D. $1\text{cm}$

Answer 1

The correct option is D $1\text{cm}$

Given,
${\ell }_2=0.62\text{m},{\ell }_1=0.2\text{m},f=400\text{Hz}$

In a resonance tube experiment, if $l_1$ and $l_2$ are the lengths of first and second resonances, then wavelength
$\lambda =2({\ell }_2-{\ell }_1)$
$\Rightarrow \lambda =2(62-20)=84\text{cm}$
Also, we know that
$l_1+e=\frac{\lambda }{4}$
where $e\to$ end correction
$\Rightarrow e=\frac{\lambda }{4}-l_1$
$\Rightarrow e=\frac{84}{4}-20=1\text{cm}$
Pressure node is formed at distance $e$ above the open end.
Thus, option (a) is the correct answer.