$A$ student is performing the experiment of a resonance column. The diameter of the column tube is $6 \, cm$. The frequency of the tuning fork is $504 \, Hz$. The speed of sound at the given temperature is $336 \, m/s$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is..........$cm$.

$A$ student is experimenting with a resonance tube apparatus in a Physics lab to find the speed of sound at room temperature. He obtained the first two resonating lengths of the air column as $17 \, cm$ and $51 \, cm$,using a tuning fork of frequency $512 \, Hz$. Find the speed of sound at room temperature in $m/s$.

Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequency of the new pipe so obtained 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.

$A$ closed organ pipe of length $L$ and an open organ pipe contain gases of densities $\rho_1$ and $\rho_2$ respectively. The compressibility of the gases is equal in both the pipes. If the frequencies of their first overtones are the same,then the length of the open organ pipe is:

$A$ tuning fork produces four beats per second with two open organ pipes having lengths $30 \ cm$ and $31 \ cm$. Find the frequency of the tuning fork in $Hz$.