An organ pipe open at one end is vibrating in its first overtone and is in resonance with another pipe open at both ends vibrating in its third harmonic. The ratio of the length of the two pipes is:

$A$ pipe $20 \; cm$ long is closed at one end. Which harmonic mode of the pipe is resonantly excited by a $430 \; Hz$ source? Will the same source be in resonance with the pipe if both ends are open? (Speed of sound in air is $340 \; m/s$).

$A$ pipe closed at one end produces a fundamental note of $412 \, Hz$. It is cut into two pieces of equal length. The fundamental notes produced by the two pieces are:

$A$ closed organ pipe of length $L_1$ and an open organ pipe contain diatomic gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibilities of the gases are same in both pipes,which are vibrating in their first overtone with the same frequency. The length of the open organ pipe is (Neglect end correction).

$A$ metre-long tube open at one end,with a movable piston at the other end,shows resonance with a fixed frequency source (a tuning fork of frequency $340\; Hz$) when the tube length is $25.5\; cm$ or $79.3\; cm$. Estimate the speed of sound (in $m/s$) in air at the temperature of the experiment. The edge effects may be neglected.

$A$ 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.