Two steel piano wires are joined end-to-end in a demonstration of wave transmission on strings. Both sections are held under the same tension by identical hanging masses, but the wires have different diameters, producing different wave speeds. The relevant properties are summarised below.
• Section I (thin wire): length 1.80m, transverse wave speed 75m/s
• Section II (thick wire): length 2.40m, transverse wave speed 50m/s
A mechanical oscillator fixed to the left end of Section I generates sinusoidal transverse waves that travel to the right.
(1) Part 1: The oscillator is set to 30.0 Hz. Calculate the wavelength of the waves while they are travelling in Section I.
(2) Part 2: Determine the wavelength of the same waves after they enter Section II. Briefly explain which property of the wave changes at the junction and which property remains the same.
(3) Part 3: At a particular instant, the entire 1.80m length of Section I contains exactly two complete wavelengths of the wave you found in part (a). At that same instant, how many complete wavelengths are simultaneously present within Section II? Show your reasoning clearly.
(4) Part 4: Discuss qualitatively, without further calculation, how the difference in wave speed between the two sections affects the rate at which mechanical energy is transmitted along each section if the wave amplitude remains unchanged. Support your discussion with appropriate physical arguments.