A longitudinal sound wave travels through air. At an instant t=0 the distance between the centres of two successive compressions is measured to be 0.85m. A microphone placed at a fixed point in the air records that successive compressions arrive at that point every 2.5ms. The maximum longitudinal displacement of air molecules from equilibrium is 0.10mm.
(i) Using the spatial information, determine the wavelength of the sound wave.
(ii) From the temporal data, calculate the time period and frequency of the wave.
(iii) Hence obtain the speed of sound in air under the given conditions.
(iv) Draw a qualitative sketch of the displacement–position graph 1.25ms later (that is, halfway through one complete oscillation). Clearly mark the positions of compressions, rarefactions, and indicate the amplitude on your diagram.
(v) Explain why the waveform drawn in part (iv) represents a shift through half a wavelength.