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 .............. $Hz$.

$A$ string of length $3 \ m$ and linear mass density $0.0025 \ kg/m$ is fixed at both ends. One of its resonance frequencies is $252 \ Hz$. The next higher resonance frequency is $336 \ Hz$. Then the fundamental frequency will be ..... $Hz$.

The pitch of an organ pipe is highest when the pipe is filled with

The end correction of a resonance column is $1 \, cm$. If the shortest length resonating with the tuning fork is $10 \, cm$,the next resonating length should be ..... $cm$.

$A$ resonance tube is old and has a jagged end. It is still used in the laboratory to determine the velocity of sound in air. $A$ tuning fork of frequency $512\,Hz$ produces the first resonance when the tube is filled with water to a mark $11\,cm$ below a reference mark,near the open end of the tube. The experiment is repeated with another fork of frequency $256\,Hz$,which produces the first resonance when water reaches a mark $27\,cm$ below the reference mark. The velocity of sound in air,obtained in the experiment,is close to .... $ms^{-1}$

$A$ 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 . . . . . . $m/s$.