Question

In a resonance column experiment, a tuning fork of frequency $400Hz$ is used. The first resonance is observed when the air column has a length of $20.0cm$ and the second resonance is observed when the air column has a length of $62.0cm$ (a) Find the speed of sound in air. (b) How much distance above the open end does the pressure node form?

• A. 336, 1
• B. 400, 3
  
• C. 500, 5
  
• D. 600, 0
  

Answer 1

The correct option is A 336, 1

Given:

length of air column at the first resonance $l_1=20cm=0.2m$

length of air column at the second resonance $l_2=62cm=0.62m$

frequency of tuning fork $f=400Hz$

$\left(a\right)$ Find the speed of sound in air

We know:

$\lambda =2\left(l_2-l_1\right)$

implies that $\lambda =2\left(62-20\right)=84cm=0.84m$

Speed of sound in air $v=\lambda f$

$v=0.84\times 400=336m/s$

Speed of the sound in air is $336m/s$.

$\left(b\right)$ distance of open node is $d$.

$l_1+d=\frac{\lambda }{4}$

implies that $d=\frac{\lambda }{4}-l_1=21-20=1cm$

distance is $1$cm