One end of a long rope is tied to a fixed vertical pole. The rope is stretched horizontally with a tension 8 N. Let us consider the length of the rope to be along X-axis. A sample harmonic oscillator at x = 0 generates a transverse wave of frequency 100 Hz and amplitude 2 cm along the rope. Mass of a unit length of the rope is 20 gm/m. Ignoring the effect of gravity, answer the following questions:
Tension in the given rope remaining the same, if a simple harmonic oscillator of frequency 200 Hz is used instead of the earlier oscillator of frequency 100 Hz, then

Options

A. speed of transverse waves in the rope will be doubled, wavelength will not change
B. speed of transverse waves in the rope will become half, wavelenfth will become one-fourth
C. speed of transverse waves in the rope will become four times, wavelength will be doubled
D. speed of transverse waves in the rope will not change, wavelength will become half

Answer

D