A sinusoidal mechanical wave is monitored using two separate graphs that a student plots in the laboratory.
The first graph is displacement (y) versus time (t) for a single particle of the medium, while the second graph is displacement (y) versus position (x) for the entire medium at a fixed instant.
Answer the following questions on the basis of these two graphs.
(i) Describe, with reasoning, how the amplitude of the wave can be obtained from the displacement–time graph for the chosen particle.
(ii) Explain the procedure for determining the period and hence the frequency of the wave from the same displacement–time graph.
(iii) The displacement–position graph shows the spatial profile of the wave at an instant. Explain clearly how the wavelength of the wave can be measured from this graph.
(iv) If both graphs are drawn on different scales, state what additional care must be taken while reporting the numerical values of amplitude, period, and wavelength.