Question

A tuning fork of frequency $340\text{Hz}$ is vibrated just above a cylindrical tube. The length of the tube is $120\text{cm}$. Water is slowly poured into the tube. Determine the minimum height of water required for resonance. (Take velocity of sound in air $\text{v}=340\text{m/s}$)

• A. $25\text{cm}$
• B. $45\text{cm}$
• C. $50\text{cm}$
• D. $75\text{cm}$

Answer 1

The correct option is B $45\text{cm}$


$f=\left(\frac{2n+1}{4L}\right).v$

$L=1.2-h$

$340=\left(\frac{2n+1}{4(1.2-h)}\right)340$

$1.2-h=\frac{2n+1}{4}$

$h=1.2-\left(\frac{2n+1}{4}\right)$

for $h$ minimum $\frac{2n+1}{4}$ has to be maximum and not more tham 1.2.

So, $n=1$
$h_{min}=0.45m=45cm$