A closed pipe of length $300 \,cm$ contains some sand. A speaker is connected at one of its ends. The frequency of the speaker at which the sand will arrange itself in $20$ equidistant piles is close to .......... $kHz$ (velocity of sound is $300 \,m / s )$
KVPY 2017, Diffcult
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$(c)$ Given is a Kundt's tube experiment. It is used today for demonstrating standing waves. $A$ standing wave is generated in tube causes small amount of chalk powder to pile up at nodes.
Distance between the piles is one half wavelength $(\frac{\lambda}{2})$ of longitudinal waves.
Now, given in $300 cm$, there are 20 piles of powder.
$\therefore \quad 20 \times \frac{\lambda}{2}=300 \Rightarrow \lambda=\frac{300}{10 \times 100} \,m$
So, frequency of sound is
$f=\frac{v}{\lambda}=\frac{300}{\left(\frac{300}{1000}\right)}=1 \,kHz$
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