A sinusoidal wave travels along a stretched string with a constant speed of 40 m s⁻¹. The amplitude of the wave is kept unchanged while the driving oscillator suddenly doubles its frequency.
(i) State the relation connecting the speed of a progressive wave with its wavelength and frequency.
(ii) If the frequency is doubled while the wave speed remains 40 m s⁻¹, what happens to the wavelength? Explain your reasoning clearly without using numerical substitution.
(iii) Will either the speed or the amplitude of the wave change because of the increase in frequency? Give a brief justification for each quantity.