Question

A tuning fork of frequency 340 Hz is sounded above an organ pipe of length 120 cm. Water is now slowly poured in it. The minimum height of water column required for resonance is (speed of sound in air $=340m/s$)

• A. 25 cm
• B. 95 cm
• C. 75 cm
• D. 45 cm

Answer 1

The correct option is D 45 cm

$f=340Hz$
$l=1.2m$
$f=\left(\frac{2n+1}{4l}\right)\sqrt{\frac{T}{4}}$
for min. height $n=1$
$340=\frac{3}{4(1.20-l^1)}\cdot 340$
$1.2-l^1=0.75$
$l^1=0.45m=45m$
$\sqrt{\frac{T}{4}}=340m/s$
here $l=120-l^1$
$l^1=$ water coloumn height.