$A$ cylindrical tube open at both ends has a fundamental frequency '$f$' in air. The tube is dipped vertically in water so that half of its length is in water. The new fundamental frequency is

$A$ closed organ pipe and an open pipe of the same length produce $4$ beats when they are set into vibrations simultaneously. If the length of each of them were twice their initial lengths,the number of beats produced will be

In a resonance tube experiment,the first resonance is obtained for $10\, cm$ of air column and the second for $32\, cm$. The end correction for this apparatus is ....$cm$

$A$ closed organ pipe and an open organ pipe of the same length produce $2$ beats per second when they are set into vibrations together in their fundamental mode. The length of the open pipe is now halved and that of the closed pipe is doubled. The number of beats produced per second will be:

$A$ person blows into the open end of a long pipe. As a result,a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe,which of the following statements are true?
$(I)$ $A$ high-pressure pulse starts travelling up the pipe,if the other end of the pipe is open.
$(II)$ $A$ low-pressure pulse starts travelling up the pipe,if the other end of the pipe is open.
$(III)$ $A$ low-pressure pulse starts travelling up the pipe,if the other end of the pipe is closed.
$(IV)$ $A$ high-pressure pulse starts travelling up the pipe,if the other end of the pipe is closed.

$A$ 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 ..... $Hz$.