The fundamental frequency of an open pipe of length $0.5 \ m$ is equal to the frequency of the first overtone of a closed pipe of length $l_c$. The value of $l_c$ in meters is:

$A$ metal rod of length $125 \ cm$ is clamped at its midpoint. If the speed of sound in the metal is $5000 \ ms^{-1}$, then the fundamental frequency of the longitudinal vibrations of the rod is (in $kHz$)

$A$ 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 $m/s$.

Which order of harmonics is missing or absent in case of stationary sound waves produced in a closed pipe?

Find the fundamental frequency of a closed pipe,if the length of the air column is $42 \, m$. (speed of sound in air $= 332 \, m/s$) (in $, Hz$)

$A$ 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?