The fundamental frequency of a closed pipe is $400 \text{ Hz}$. If $\left(\frac{1}{3}\right)^{rd}$ length of the pipe is filled with water, the frequency of the $2^{\text{nd}}$ harmonic of the pipe will be (Neglect end correction). (in $\text{ Hz}$)

The frequency of the third overtone of a pipe of length $L_c$,closed at one end,is the same as the frequency of the sixth overtone of a pipe of length $L_o$,open at both ends. Then the ratio $L_c : L_o$ is

In a closed organ pipe, the number of nodes formed in the fifth and ninth harmonics are respectively:

On producing waves of frequency $1000 \text{ Hz}$ in a Kundt's tube,the total distance between $6$ successive nodes is $85 \text{ cm}$. The speed of sound in the gas filled in the tube is ..... $m/s$.

$A$ tuning fork of frequency $480\, Hz$ is used in an experiment for measuring the speed of sound $(\nu)$ in air by the resonance tube method. Resonance is observed to occur at two successive lengths of the air column,$\ell_1 = 30\, cm$ and $\ell_2 = 70\, cm$. Then $\nu$ is equal to ..... $m/s$.

$A$ 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 $300 \,m/s$).