$A$ pipe $60 \ cm$ long and open at both ends produces harmonics. Which harmonic mode of the pipe resonates with a $2.2 \ kHz$ source? (Speed of sound in air $= 330 \ m/s$) (Neglect end correction)

The stationary wave $y = 2a \sin kx \cos \omega t$ in a closed organ pipe is the result of the superposition of $y = a \sin (\omega t - kx)$ and

An open pipe is in resonance in its $2^{nd}$ harmonic with a tuning fork of frequency ${f_1}$. Now,it is closed at one end. If the frequency of the tuning fork is increased slowly from ${f_1}$,then again a resonance is obtained with a frequency ${f_2}$. If in this case the pipe vibrates in its $n^{th}$ harmonic,then:

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:

$A$ 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?

In the fundamental mode,the time required for a sound wave to reach the closed end of an air-filled pipe is $t$ seconds. What is the frequency of vibration of the air column?