A tuning fork of frequency 340 ,Hz resonates in the fundamental m… - Vidyadip

MCQ

A tuning fork of frequency $340\,Hz$ resonates in the fundamental mode with an air column of length $125\,cm$ in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is________ $cm$

(Velocity of sound in air is $340\,ms ^{-1}$ )

A
$48$
B
$49$
✓
$50$
D
$54$

✓

Answer

Correct option: C.

$50$

c
Assumption : Ignore word "fundamental mode" in question.

$\lambda=\frac{ V }{ f }=\frac{340}{340}=1\,m$

First resonating length $=\frac{\lambda}{4}=25\,cm$

Second resonating length $=\frac{3 \lambda}{4}=75\,cm$

Third resonating length $=\frac{5 \lambda}{4}=125\,cm$

Height of water required $=125-75=50\,cm$

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