One end of a long and thin rope, stretched horizontally with a tension $$T = 8\,\text{N}$$ along $$x$$ axis, is supporting a weight after passing over a pulley fixed on a vertical pole, see figure. At the other end, a simple harmonic oscillator at $$x = 0$$ generates a transverse wave of frequency $$100\,\text{Hz}$$ and an amplitude of $$2\,\text{cm}$$ in the rope. The wave propagates along the rope. The mass per unit length of the rope is $$20\,\text{g m}^{-1}$$. Ignoring the effect of gravity on the rope, the correct option or options is or are

Wavelength of the transverse wave is $$20\,\text{cm}$$

Maximum magnitude of transverse acceleration of any point on the rope is nearly $$800\,\text{m s}^{-2}$$

If the oscillator produces maximum negative displacement at $$x = 0$$ at time $$t = 0$$, the equation of the wave can be expressed as $$y(x,t) = -0.02\sin\left(10\pi x - 100\pi t\right)$$ in SI units

Tension in the given rope remaining unchanged, if a harmonic oscillator of frequency $$200\,\text{Hz}$$ is used instead of earlier frequency $$100\,\text{Hz}$$, the wavelength will be $$10\,\text{cm}$$