The fundamental frequency of a closed pipe is $220 \ Hz$. If $\frac{1}{4}$ of the pipe is filled with water,the frequency of the first overtone of the pipe now is ..... $Hz$.

In the $5$th overtone of an open organ pipe,the number of nodes $(N)$ and antinodes $(A)$ are:

$A$ whistle whose air column is open at both ends has a fundamental frequency of $5100 \ Hz$. If the speed of sound in air is $340 \ ms^{-1}$,the length of the whistle,in $cm$,is

For a certain organ pipe,three successive resonance frequencies are observed at $425 \, Hz$,$595 \, Hz$,and $765 \, Hz$ respectively. If the speed of sound in air is $340 \, m/s$,then the length of the pipe is ..... $m$.

Two open organ pipes of length $50 \, cm$ and $50.5 \, cm$ produce $3$ beats per second. The velocity of sound is ..... $m/s$.

In an open organ pipe,$v_3$ and $v_6$ are the $3^{\text{rd}}$ and $6^{\text{th}}$ harmonic frequencies,respectively. If $v_6 - v_3 = 2200 \text{ Hz}$,then the length of the pipe is . . . . . . mm. (Take the velocity of sound in air as $330 \text{ m/s}$.)