A sinusoidal wave of frequency 256Hz is generated at one end of a long composite string made by knotting together three uniform strings of different linear mass densities. In each portion of the string, the tension is kept at 64N. The wave travels from section I to section II and then to section III without reflection.
(a) Given that the linear mass densities of the three sections are μ1=4.0×10−3kgm−1, μ2=9.0×10−3kgm−1 and μ3=1.6×10−2kgm−1 respectively, calculate the speed of the wave in each section.
(b) Determine the wavelength in each section.
(c) Show that the product of wavelength and square root of linear mass density is the same for all three sections under the given conditions.
(d) Explain physically why this invariance is expected when the frequency is fixed by the source and the tension is uniform.