An elastic string AB is joined to a toy slinky BC and laid straight on a long laboratory bench. A student simultaneously gives end A a sharp upward jerk, producing a transverse crest that travels to point B, and pushes end C forward, producing a longitudinal compression that travels to point B.
The crest travels 1.2m along AB in 0.8s and has an amplitude of 5cm. Successive crests that follow are spaced 40cm apart. The compression travels 0.9m along BC in 0.6s, and successive compressions are spaced 30cm apart.
(a) Calculate the speed of the transverse wave in segment AB and the speed of the longitudinal wave in segment BC.
(b) Determine the frequency of each wave.
(c) On a single, well-labelled sketch, show at least two wavelengths of the transverse wave and two wavelengths of the longitudinal wave side by side, clearly marking crest, trough, compression, rarefaction and amplitude where appropriate.
(d) The energy transported by a wave is proportional to the square of its amplitude. Using this information, compare quantitatively the energy transported by the transverse wave with the energy that would be transported by another transverse wave on the same string having an amplitude of 2.5cm.