In a large room,a person receives direct sound waves from a source $120 \ m$ away from him. He also receives waves from the same source which reach him after being reflected from the $25 \ m$ high ceiling at a point halfway between them. The two waves interfere constructively for wavelengths of

$A$ rod of length $L$ and negligible mass is suspended by two identical strings $AB$ and $CD$ as shown in the figure. $A$ mass $M$ is suspended from point $O$ which is at a distance $x$ from $B$. If the frequency of the first harmonic of $AB$ is equal to the frequency of the second harmonic of $CD$, then the value of $x$ is

The frequency of a stretched uniform wire of length $L$ under tension is in resonance with the fundamental frequency of a closed pipe of same length. If the tension in the wire is increased by $8 \ N$,it is in resonance with the first overtone of the same closed pipe. The initial tension in the wire is (in $N$)

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 ........

$A$ 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 ...... .