A narrow steel wire is stretched tightly between two rigid supports. A tuning fork of frequency 512 Hz is held near one end of the wire and produces a progressive transverse wave along the wire.
(a) If the wave speed on the wire is 256 m s−1, calculate the wavelength of the wave on the wire.
(b) The same tuning fork is now sounded with the lower half of the wire immersed in water, where the wave speed along that part of the wire becomes 320 m s−1. Assuming the frequency remains unchanged, determine the new wavelength of the wave in the immersed portion.
(c) Identify which of the quantities—frequency, wavelength, wave speed—changed between parts (a) and (b), and explain why in each case.