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 $A$?

$A$ pipe closed at one end has a length of $0.8 \ m$. At its open end,a $0.5 \ m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \ N$ and the speed of sound is $320 \ m/s$,the mass of the string is: (in $g$)

Two superimposing waves are represented by the equations $y_1 = 2 \sin 2 \pi(10 t - 0.4 x)$ and $y_2 = 4 \sin 2 \pi(20 t - 0.8 x)$. The ratio of $I_{\max}$ to $I_{\min}$ is ........

$A$ 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 at a right angle 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 the point $D$ where a detector is placed. If a minimum is formed at the detector,then the magnitude of the wavelength $\lambda$ of the wave produced is given by:

In Quincke's tube,a detector detects minimum intensity. Now,one of the tubes is displaced by $5 \, cm$. During displacement,the detector detects maximum intensity $10$ times,and finally a minimum intensity (when displacement is complete). The wavelength of sound is .... $cm$.

$Assertion :$ Transverse waves are produced in a very long string fixed at one end. Only a progressive wave is observed near the free end.
$Reason :$ Energy of the reflected wave does not reach the free end.