If $T$ is the reverberation time of an auditorium of volume $V$,then:

Given below are some functions of $x$ and $t$ to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent $(i)$ a travelling wave,$(ii)$ a stationary wave or $(iii)$ none at all:
$(a)$ $y = 2 \cos(3x) \sin(10t)$
$(b)$ $y = 2 \sqrt{x - vt}$
$(c)$ $y = 3 \sin(5x - 0.5t) + 4 \cos(5x - 0.5t)$
$(d)$ $y = \cos x \sin t + \cos 2x \sin 2t$

$A$ clamped string is oscillating in the $n^{th}$ harmonic,then

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 ........

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):

$A$ 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 $g$)