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 $kg$.

Fill in the blanks:
$(i)$ For humans,the minimum wavelength of a sound wave in the audible range is nearly ...... .
$(ii)$ Only ...... waves can be propagated by a fluid medium.
$(iii)$ The distance travelled by a travelling wave having wavelength $\lambda$ and periodic time $T$,in one second is ...... .

Two tuning forks $A$ and $B$ give $5$ beats per second. Fork $A$ resonates with a closed air column $20 \ cm$ long and fork $B$ with an open air column $40.5 \ cm$ long. Neglecting end correction,the frequencies of tuning forks $A$ and $B$ are respectively.

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

$A$ pulse shown here is reflected from the rigid wall $A$ and then from the free end $B$. The shape of the string after these $2$ reflections will be