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Q. A resonance air column of length $20\, cm$ resonates with a tuning fork of frequency $450\, Hz$. Ignoring the correction, the velocity of sound in air will be

AIIMSAIIMS 1999Waves

Solution:

We know that the minimum length of the air column in a resonance tube corresponds to the fundamental mode of vibrations. Hence by ignoring end correction.
$l=\frac{\lambda}{4} $
$\Rightarrow \lambda=4 l=4 \times 20=80 \,cm =0.8\, m$
Resonant frequency $u=450\, Hz$
$\therefore $ Speed of sound $v=v \lambda$
$=450 \times 0.8=360 \,m / s$