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 $\,Hz$)

$A$ pipe open at both ends of length $1.5 \,m$ is dipped in water such that the second overtone of the vibrating air column resonates with a tuning fork of frequency $330 \,Hz$. If the speed of sound in air is $330 \,m/s$, then the length of the pipe immersed in water is (Neglect end correction). (in $\,m$)

Obtain the equation for the frequency of a stationary wave produced in an open pipe and show that all harmonics are possible in it.

$A$ cylindrical tube,open at both ends,has a fundamental frequency $f_0$ in air. The tube is dipped vertically into water such that half of its length is inside water. The fundamental frequency of the air column now is

In a $1 \ m$ long open pipe,what is the harmonic of resonance obtained with a tuning fork of frequency $480 \ Hz$? (Assume the speed of sound $v = 330 \ m/s$)

$A$ closed organ pipe and an open organ pipe of the same length produce $2 \text{ beats/second}$ while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of the closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is