For a certain organ pipe,three successive resonance frequencies are observed at $425 \, Hz, 595 \, Hz,$ and $765 \, Hz$ respectively. Taking the speed of sound in air to be $340 \, m/s$,the fundamental frequency of the pipe (in $Hz$) is:

$A$ 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.

The frequency of the first overtone of a closed pipe of length $l_{1}$ is equal to that of the first overtone of an open pipe of length $l_{2}$. The ratio of their lengths $(l_{1}: l_{2})$ is

The first overtone of the vibrating air column of a closed pipe has the same frequency as the second overtone of an open pipe $1.5 \ m$ long. The length of the closed pipe is (in $m$)

$A$ closed organ pipe of length $1.2 \, m$ vibrates in its first overtone mode. The pressure variation is maximum at:

The second overtone of an open organ pipe has the same frequency as the first overtone of a closed organ pipe $L$ metre long. The length of the open pipe will be: