Consider a system of three connected strings, $S_1, S_2$ and $S_3$ with uniform linear mass densities $\mu$ $\mathrm{kg} / \mathrm{m}, 4 \mu \mathrm{~kg} / \mathrm{m}$ and $16 \mu \mathrm{~kg} / \mathrm{m}$, respectively, as shown in the figure. $S_1$ and $S_2$ are connected at the point $P$, whereas $S_2$ and $S_3$ are connected at the point $Q$, and the other end of $S_3$ is connected to a wall. A wave generator 0 is connected to the free end of $S_1$. The wave from the generator is represented by $y=y_0 \cos (\omega t-k x) \mathrm{cm}$, where $y_0, \omega$ and $k$ are constants of appropriate dimensions. Which of the following statements is/are correct:

A person sitting inside an elevator performs a weighing experiment with an object of mass 50 kg . Suppose that the variation of the height $y$ (in m ) of the elevator, from the ground, with time $t$ (in s) is given by $y=8\left[1+\sin \left(\frac{2 \pi t}{T}\right)\right]$, where $T=40 \pi \mathrm{~s}$. Taking acceleration due to gravity, $g=10$ $\mathrm{m} / \mathrm{s}^2$, the maximum variation of the object's weight (in N ) as observed in the experiment is ___________.

A cube of unit volume contains $35 \times 10^7$ photons of frequency $10^{15} \mathrm{~Hz}$. If the energy of all the photons is viewed as the average energy being contained in the electromagnetic waves within the same volume, then the amplitude of the magnetic field is $\alpha \times 10^{-9} \mathrm{~T}$. Taking permeability of free space $\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}$, Planck's constant $h=6 \times 10^{-34} \mathrm{Js}$ and $\pi=\frac{22}{7}$, the value of $\alpha$ is ____________.

Two identical plates P and Q , radiating as perfect black bodies, are kept in vacuum at constant absolute temperatures $\mathrm{T}_{\mathrm{P}}$ and $\mathrm{T}_{\mathrm{Q}}$, respectively, with $\mathrm{T}_{\mathrm{Q}}<\mathrm{T}_{\mathrm{P}}$, as shown in Fig. 1. The radiated power transferred per unit area from P to Q is $W_0$. Subsequently, two more plates, identical to P and Q , are introduced between P and Q, as shown in Fig. 2. Assume that heat transfer takes place only between adjacent plates. If the power transferred per unit area in the direction from $P$ to $Q$ (Fig. 2) in the steady state is $W_S$, then the ratio $\frac{W_0}{W_S}$ is ________.