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:

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 ....$cm$

$A$ glass tube is open at both ends. $A$ tuning fork of frequency $f$ resonates with the air column inside the tube. Now,the tube is placed vertically inside water so that half the length of the tube is filled with water. Now,the air column inside the tube is in unison with another fork of frequency $f^{\prime}$. Then,

The fundamental frequency of a closed pipe is $220 \ Hz$. If $\frac{1}{4}$ of the pipe is filled with water,the frequency of the first overtone of the pipe now is ..... $Hz$.

$A$ tuning fork vibrating with a frequency of $512$ $Hz$ is kept close to the open end of a tube filled with water. The water level in the tube is gradually lowered. When the water level is $17$ $cm$ below the open end,maximum intensity of sound is heard. If the room temperature is $20^{\circ} C$,calculate:
$(a)$ Speed of sound in air at room temperature.
$(b)$ Speed of sound in air at $0^{\circ} C$.
$(c)$ If the water in the tube is replaced with mercury,will there be any difference in your observations?

$A$ 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: