$A$ closed organ pipe $150 \ cm$ long gives $7$ beats per second with an open organ pipe of length $350 \ cm$,both vibrating in fundamental mode. The velocity of sound is . . . . . . $m/s$.

On closing an open organ pipe from one end, it is noticed that the frequency of the third harmonic is $50 \,Hz$ more than the fundamental frequency of vibration in the open organ pipe. The fundamental frequency of the open organ pipe is (in $\,Hz$)

$A$ closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio

An open pipe of length $l$ vibrates in its fundamental mode. The pressure variation is maximum at

Two open organ pipes of length $60 \,cm$ and $90 \,cm$ resonate at $6^{\text{th}}$ and $5^{\text{th}}$ harmonics respectively. The difference of frequencies for the given modes is . . . . . $Hz$.
(Velocity of sound in air $= 333 \,m/s$)