$A$ pipe of length $85\, cm$ is closed from one end. Find the number of possible natural oscillations of the air column in the pipe whose frequencies lie below $1250\, Hz$. The velocity of sound in air is $340\, m/s$.

Two open organ pipes of lengths $50 \,cm$ and $51 \,cm$ are totally immersed in a medium. They are found to give $40$ beats in $10 \,s$ when each is sounding at its fundamental note. The speed of sound in this medium is (in $\,ms^{-1}$)

An open organ pipe is closed at one end such that the third overtone of the closed pipe is found to be higher in frequency by $200 \ Hz$ than the second overtone of the original open pipe. The fundamental frequency of the open pipe is (Neglect end correction). (in $Hz$)

An open tube is in resonance with a string (frequency of vibration of the tube is $n_0$). If the tube is dipped in water so that $75\%$ of the length of the tube is inside the water,then the ratio of the frequency of the tube to the string now will be

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

$A$ closed pipe is in resonance with a tuning fork at $27^{\circ} C$ when its length is $20 \,cm$. If the pipe is to be in resonance with the same tuning fork at $7^{\circ} C$, then the change in the length of the pipe required is nearly: (in $\,mm$)