$A$ wave pulse on a string has the dimensions shown in the figure. The wave speed is $v = 1 \, cm/s$. If point $O$ is a free end,what is the shape of the wave at time $t = 3 \, s$?

An auditorium has a volume of $10^5 \ m^3$ and a surface area of absorption of $2 \times 10^4 \ m^2$. Its average absorption coefficient is $0.2$. The reverberation time of the auditorium in seconds is:

$A$ pipe open at one end has a length of $0.8 \text{ m}$. At the open end of the tube, a string $0.5 \text{ m}$ long is vibrating in its first overtone and resonates with the fundamental frequency of the pipe. If the tension in the string is $50 \text{ N}$, what is the mass of the string (in $\text{ g}$)? (Neglect end correction, Speed of sound = $320 \text{ m/s}$)

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 .... $cm$.

$A$ wire of linear mass density $\mu = 9.8 \times 10^{-3} \, kg \, m^{-1}$ passes over a frictionless light pulley fixed on the top of a frictionless inclined plane which makes an angle of $30^{\circ}$ with the horizontal. Masses $m$ and $M$ are tied at the two ends of the wire such that $m$ rests on the plane and $M$ hangs freely vertically downwards. The entire system is in equilibrium and a transverse wave propagates along the wire with a velocity of $100 \, m \, s^{-1}$. Choose the correct option for $m$ in $kg$.

$A$ 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 $g$)