An air column in a tube $32 \,cm$ long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length $66 \,cm$ is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce $8$ beats per second. Then the frequencies of the two tuning forks are (Consider fundamental frequencies only):

$A$ 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

$Assertion :$ 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.

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

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 .... $km$.

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions at a right angle to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at the point $D$ where a detector is placed. If a minimum is formed at the detector,then the magnitude of the wavelength $\lambda$ of the wave produced is given by: