In a resonance tube,the first and second resonances are obtained at depths $22.7 \,cm$ and $70.2 \,cm$ respectively. The third resonance will be obtained at a depth of: (in $\,cm$)

In an organ pipe closed at one end,the sum of the frequencies of the first three overtones is $3930 \ Hz$. The frequency of the fundamental mode of the organ pipe is: (in $Hz$)

An organ pipe $P_1$ closed at one end is vibrating in its first overtone. Another pipe $P_2$ open at both ends is vibrating in its third overtone. They are in resonance with a given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is:

$A$ closed pipe of length $300 \,cm$ contains some sand. $A$ speaker is connected at one of its ends. The frequency of the speaker at which the sand will arrange itself in $20$ equidistant piles is close to .......... $kHz$ (velocity of sound is $300 \,m/s$).

$A$ sufficiently long closed organ pipe has a small hole at its bottom. Initially,the pipe is empty. Water is poured into the pipe at a constant rate. The fundamental frequency of the air column in the pipe

In the fundamental mode, the time required for a sound wave to reach the closed end of a pipe filled with air is $t$ seconds. What is the frequency of vibration of the air column? ($\lambda$ = wavelength of the wave)