The fundamental frequency of a closed pipe is $400 \text{ Hz}$. If $\left(\frac{1}{3}\right)^{rd}$ length of the pipe is filled with water, the frequency of the $2^{\text{nd}}$ harmonic of the pipe will be (Neglect end correction). (in $\text{ Hz}$)

$A$ 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.

$A$ closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. What is the ratio of their lengths?

What should be the length of a closed pipe to produce resonance with a sound wave of wavelength $62 \,cm$,in fundamental mode (in $\,cm$)? [Neglect end correction]

If the length of a closed organ pipe is $1.5 \, m$ and the velocity of sound is $330 \, m/s$,then the frequency for the second note is ... $Hz$.

The first overtone frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. Further,the $n^{th}$ harmonic of the closed organ pipe is also equal to the $m^{th}$ harmonic of the open pipe,where $n$ and $m$ are: