An air column in a tube $32 \,cm$ long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length $66 \,cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):

The time of reverberation of a room $A$ is $1 \; s$. What will be the time (in seconds) of reverberation of a room,having all the dimensions double of those of room $A$?

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions right-angled to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at point $D$ where a detector is placed. If a maxima is formed at the detector,then the possible values for the wavelength $\lambda$ of the wave produced are given by:

State whether the following statements are True or False:
$(i)$ Compared to moist air,the speed of sound is greater in dry air.
$(ii)$ When the prongs of a tuning fork are rubbed,its frequency decreases.
$(iii)$ In the case of a stationary wave,the amplitudes of particles in any one loop are the same.
$(iv)$ In the case of a stationary wave,the amplitude of a particle decreases from node to antinode.

Column $I$ shows four systems,each of the same length $L$,for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency,whose wavelength is denoted as $\lambda_{f}$. Match each system with statements given in Column $II$ describing the nature and wavelength of the standing waves.
Column $I$:
$(A)$ Pipe closed at one end
$(B)$ Pipe open at both ends
$(C)$ Stretched wire clamped at both ends
$(D)$ Stretched wire clamped at both ends and at mid-point
Column $II$:
$(p)$ Longitudinal waves
$(q)$ Transverse waves
$(r)$ $\lambda_{f} = L$
$(s)$ $\lambda_{f} = 2L$
$(t)$ $\lambda_{f} = 4L$

When the tense wire of a sitar is pulled slightly from the middle and then released,which type of waves are produced?