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 ..........

Match Column-$1$ with Column-$2$.

Column-$1$	Column-$2$
$(a)$ Light waves	$(i)$ Mechanical and transverse.
$(b)$ Sound waves	$(ii)$ Mechanical and longitudinal.
$(c)$ Earthquake waves	$(iii)$ Non-mechanical and transverse.
$(d)$ Waves on a tense string	$(iv)$ Mechanical,transverse and longitudinal.

Match the following List-$I$ with List-$II$.

List-$I$	List-$II$
$(A)$ Transverse wave	$(i)$ Vibrations parallel to the direction of propagation
$(B)$ Longitudinal wave	$(ii)$ Vibrations perpendicular to the direction of propagation
$(C)$ Beats	$(iii)$ Superposition of waves travelling in the opposite directions
$(D)$ Stationary waves	$(iv)$ Superposition of waves travelling in same direction

The correct answer is

An earthquake generates both transverse $(S)$ and longitudinal $(P)$ waves in the Earth. The speed of $S$ waves is about $4.5 \, km/s$ and that of $P$ waves is about $8.0 \, km/s$. $A$ seismograph records $P$ and $S$ waves from an earthquake. The first $P$ wave arrives $4.0 \, min$ before the first $S$ wave. The epicenter of the earthquake is located at a distance of about .... $km$.

$A$ 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

$A$ clamped string is oscillating in the $n^{th}$ harmonic,then