$Assertion :$ Sound waves cannot travel in vacuum but light can travel in vacuum.
$Reason :$ Sound waves are longitudinal waves and they cannot be polarised but electromagnetic waves are transverse and they can be polarised.

An object of density $2000 \ kg \ m^{-3}$ is hung from a thin light wire. The fundamental frequency of the transverse waves in the wire is $200 \ Hz$. If the object is immersed in water such that half of its volume is submerged,then the fundamental frequency of the transverse waves in the wire is (in $Hz$)

$Assertion :$ Transverse waves are produced in a very long string fixed at one end. Only a progressive wave is observed near the free end.
$Reason :$ Energy of the reflected wave does not reach the free end.

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 .... $km$.

$A$ pipe closed at one end has a length of $0.8 \,m$. At its open end, a $0.5 \,m$ long uniform string is vibrating in its $2^{nd}$ harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \,N$ and the speed of sound is $320 \,m/s$, what is the mass of the string (in $\,g$)?

Two uniform strings of mass per unit length $\mu$ and $4 \mu$,and length $L$ and $2 L$,respectively,are joined at point $O$,and tied at two fixed ends $P$ and $Q$,as shown in the figure. The strings are under a uniform tension $T$. If we define the frequency $v_0=\frac{1}{2 L} \sqrt{\frac{T}{\mu}}$,which of the following statement$(s)$ is(are) correct?
$(A)$ With a node at $O$,the minimum frequency of vibration of the composite string is $v_0$
$(B)$ With an antinode at $O$,the minimum frequency of vibration of the composite string is $2 v_0$
$(C)$ When the composite string vibrates at the minimum frequency with a node at $O$,it has $6$ nodes,including the end nodes
$(D)$ No vibrational mode with an antinode at $O$ is possible for the composite string