$A$ closed organ pipe and an open pipe of the same length produce $4$ beats when they are set into vibrations simultaneously. If the length of each of them were twice their initial lengths,the number of beats produced will be

The first overtone of the vibrating air column of a closed pipe has the same frequency as the second overtone of an open pipe $1.5 \ m$ long. The length of the closed pipe is (in $m$)

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

$A$ string fixed at both ends is in resonance in its $2^{nd}$ harmonic with a tuning fork of frequency $f_1$. Now,one end becomes free. If the frequency of the tuning fork is increased slowly from $f_1$,then again a resonance is obtained when the frequency is $f_2$. If in this case the string vibrates in the $n^{th}$ harmonic,then:

An organ pipe with both ends open has a length $L=25 \,cm$. An extra hole is created at position $\frac{L}{2}$. The lowest frequency of sound produced is (assume,speed of sound $=340 \,m/s$) (in $\,Hz$)

If $L_1$ and $L_2$ are the lengths of the first and second resonating air columns in a resonance tube,then the wavelength of the note produced is