$Assertion :$ 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.

Four different independent waves are represented by $(i)$ $y_1 = a_1 \sin \omega t$,$(ii)$ $y_2 = a_2 \sin 2\omega t$,$(iii)$ $y_3 = a_3 \cos \omega t$,and $(iv)$ $y_4 = a_4 \sin (\omega t + \frac{\pi}{3})$. With which two waves is interference possible?

Column $I$ shows four systems,each of the same length $L$,for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency,whose wavelength is denoted as $\lambda_{f}$. Match each system with statements given in Column $II$ describing the nature and wavelength of the standing waves.
Column $I$:
$(A)$ Pipe closed at one end
$(B)$ Pipe open at both ends
$(C)$ Stretched wire clamped at both ends
$(D)$ Stretched wire clamped at both ends and at mid-point
Column $II$:
$(p)$ Longitudinal waves
$(q)$ Transverse waves
$(r)$ $\lambda_{f} = L$
$(s)$ $\lambda_{f} = 2L$
$(t)$ $\lambda_{f} = 4L$

At a certain moment, the photograph of a string on which a harmonic wave is travelling to the right is shown. Then, which of the following is true regarding the velocities of the points $P$, $Q$ and $R$ on the string?

Which of the following graphs is/are correct?

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