$A$ 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 .... $m$

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

$A$ 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 $kg$.

The ratio of intensities between two coherent sound sources is $4:1$. The difference of loudness in $dB$ between maximum and minimum intensities when they interfere in the space is ..........

$A$ composite string is made up by joining two strings of different masses per unit length $\mu$ and $4\mu$. The composite string is under the same tension. $A$ transverse wave pulse $Y = (6 \text{ mm}) \sin(5t + 40x)$,where $t$ is in seconds and $x$ in meters,is sent along the lighter string towards the joint. The percentage of power transmitted to the heavier string through the joint is approximately ..... $\%$

$A$ 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