I am reading a book about wave mechanics. There are two different cord (one light and one heavy) connected together, one person waving the lighter one, the wave transverse to the right from the lighter one to the heavy one. The frequency and the wavelength is given so the speed and the tension of the lighter cord are unknown. The textbook stated that when the wave traveled into the heavier cord, the tension and the frequency doesn't change. But I am wondering why the tension as well as the frequency stay unchanged? Why not the wavelength stay unchanged? What's the physical explanation of it?
The tension in the two cords is the same because they are tied together. For example if the tension in the thick cord was higher than the thin cord the thick cord would shrink and the thin cord stretch until the tensions were equal again.
The frequency has to be the same in both cords because the phase of the wave has to match at the junction between the cords. For example if the wave in the thin cord is zero at some time $t$ the wave in the thick cord must also be zero at the junction at the same time otherwise there would eb a discontinuity in the cords at the junction. If the waves in the two cords had different frequencies the phase difference at the junction would be continually changing and you'd get discontinuities.