$A$ 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

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:

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.

$A$ man standing in front of a mountain beats a drum at regular intervals. The rate of drumming is gradually increased and he finds that the echo is not heard distinctly when the rate becomes $40$ per minute. He then moves nearer to the mountain by $90 \ m$ and finds that the echo is again not heard when the drumming rate becomes $60$ per minute. The distance between the mountain and the initial position of the man is .... $m$

$A$ vibrating string of certain length $l$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75 \ cm$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $n$. Now,when the tension of the string is slightly increased,the number of beats reduces to $2$ per second. Assuming the velocity of sound in air to be $340 \ m/s$,the frequency $n$ of the tuning fork in $Hz$ is: