Transverse waves are being generated on a rope under constant tension. Determine the factor by which the required power is changed in each of the following situations.
(a) Both the length of the rope and the wavelength are halved.
(b) The length of the rope is doubled, and the angular frequency remains constant.
(c) Both the wavelength and the amplitude are doubled.
(d) The amplitude is doubled, and the angular frequency is halved.