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?

Select the correct alternative$(s)$ :-
$(A)$ Number of nodes equals to number of antinodes in closed organ pipe.
$(B)$ In open organ pipe,if number of antinodes is $m$,then number of nodes will be $m-1$.
$(C)$ If frequency of $4^{\text{th}}$ harmonic of open organ pipe is $400 \ Hz$,then frequency of $2^{\text{nd}}$ overtone of closed organ pipe of same length is $250 \ Hz$.
$(D)$ Time interval between successive maxima or minima (for superposition of two waves) is $\Delta t = \frac{1}{|f_1-f_2|} \ s$.

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?

$A$ wave equation is given as $y = \cos(500t - 70x)$,where $y$ is in $mm$,$x$ is in $m$,and $t$ is in $s$. Which of the following statements is correct?

State whether the following statements are True or False:
$(i)$ Compared to moist air,the speed of sound is greater in dry air.
$(ii)$ When the prongs of a tuning fork are rubbed,its frequency decreases.
$(iii)$ In the case of a stationary wave,the amplitudes of particles in any one loop are the same.
$(iv)$ In the case of a stationary wave,the amplitude of a particle decreases from node to antinode.

$A$ composite string is made up by joining two strings of different masses per unit length $\mu$ and $4\mu$. The composite string is under the same tension. $A$ transverse wave pulse $Y = (6 \text{ mm}) \sin(5t + 40x)$,where $t$ is in seconds and $x$ in meters,is sent along the lighter string towards the joint. The percentage of power transmitted to the heavier string through the joint is approximately ..... $\%$