The fundamental frequency of a closed organ pipe of length $20\; cm$ is equal to the second overtone of an organ pipe open at both the ends. The length of the organ pipe open at both the ends is ...... $cm$.

$A$ uniform tube of length $60.5\,cm$ is held vertically with its lower end dipped in water. $A$ sound source of frequency $500\,Hz$ sends sound waves into the tube. When the length of tube above water is $16\,cm$ and again when it is $50\,cm,$ the tube resonates with the source of sound. Two lowest frequencies (in $Hz$),to which the tube will resonate when it is taken out of water,are (approximately).

In a resonance tube,the first resonance with a tuning fork occurs at $16 \ cm$ and the second at $49 \ cm$. If the velocity of sound is $330 \ m/s$,the frequency of the tuning fork is: (in $Hz$)

An aluminium rod having a length $100 \,cm$ is clamped at its middle point and set into longitudinal vibrations. Let the rod vibrate in its fundamental mode. The density of aluminium is $2600 \,kg/m^3$ and its Young's modulus is $7.8 \times 10^{10} \,N/m^2$. The frequency of the sound produced is .............. $Hz$.

In an organ pipe whose one end is at $x = 0$,the pressure is expressed by $p = p_0 \cos \frac{3\pi x}{2} \sin 300\pi t$,where $x$ is in meters and $t$ is in seconds. The organ pipe can be:

If $l_1$ and $l_2$ are the lengths of the air column for the first and second resonance when a tuning fork of frequency $n$ is sounded on a resonance tube,then the distance of the displacement antinode from the top end of the resonance tube is: