Question

In a resonance column experiment, a tuning fork of frequency $850\text{Hz}$ is used. The first resonance is observed when the air column has a length of $9\text{cm}$ and the second resonance is observed when the air column has a length of $29\text{cm}$. The pressure node is formed at distance $X$ above the open end. Then, value of $X$ is

• A. $0.5\text{cm}$
• B. $1\text{cm}$
• C. $2\text{cm}$
• D. $4\text{cm}$

Answer 1

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

Given that,

First resonance is observed when $l_1=9\text{cm}$

Second resonance is observed when $l_2=29\text{cm}$

Frequency of fork, $f=850\text{Hz}$


Assume that $d$ is the distance between the top of the column and the pressure node and $\lambda$ is the wavelength of the wave.

From resonance column experiment
$l_1+e=\frac{\lambda }{4}$ ...(i) (for first resonance)

$l_2+e=\frac{3\lambda }{4}$ ...(ii) (for second resonance)

$\Rightarrow l_2-l_1=\frac{\lambda }{2}$ [from equation (i) & (ii)]

$\Rightarrow \lambda =2(l_2-l_1)=2(29-9)=40\text{cm}$

Substituting the value of $\lambda$ in equation (i),
$9+e=\frac{40}{4}=10\Rightarrow e=1\text{cm}$
$\Rightarrow e=X=1\text{cm}$

So, pressure node is formed at $1\text{cm}$ above the open end.