A solid aluminium rod of length 1.20m is rigidly fixed at one end. When the free end is tapped with a hammer, a longitudinal pulse travels along the rod with speed v1=5100ms−1. Simultaneously, a light cotton string of the same length is stretched tightly alongside the rod; a small transverse pulse is generated on the string at the moment the rod is struck, the pulse travelling with speed v2=200ms−1.
(a) Derive an expression for the time difference Δt between the arrivals of the two pulses at the fixed end of the arrangement in terms of the common length L and their respective speeds v1 and v2.
(b) Using the given numerical data, calculate Δt.
(c) Explain, with reference to particle motion, why the speeds v1 and v2 differ so widely even though the pulses travel the same distance.
(d) State which of the two pulses, if any, can be polarised and justify your answer.
(e) Name one primary physical factor that determines the speed of (i) the longitudinal wave in the rod and (ii) the transverse wave on the string.