In a ripple tank, water surface waves are produced by an oscillator whose frequency can be varied. At a frequency of 10 Hz, the observed wavelength is 1.2 cm. The frequency is increased until the wavelength becomes 0.8 cm.
(a) Calculate the speed of the water waves at 10 Hz.
(b) Determine the frequency at which the wavelength becomes 0.8 cm.
(c) Keeping the oscillator at the frequency found in part (b), glycerine is added so that the wave speed is reduced by 25 %. Find the new wavelength in glycerine.
(d) Explain qualitatively why the frequency of the waves remains unchanged when the medium is changed, but the wavelength varies.