A progressive wave travelling along the positive x-axis is studied at the laboratory bench. Two separate oscilloscope traces are obtained for the same wave:
• At x=0, the displacement–time graph shows zero displacement at t=0 with a positive slope; the first crest of +5.0mm appears at t=2.0ms.
• At t=0, the displacement–position graph shows zero displacement at x=0 with a negative slope; the first crest of +5.0mm occurs at x=0.60m.
Using only these observations, answer the following.
(i) State the amplitude of the wave and justify your answer.
(ii) Calculate the period and the angular frequency.
(iii) Determine the wavelength and the wave number.
(iv) Decide whether the initial phase constant ϕ is positive or negative. Give reasons based on the signs of the initial slopes of the two graphs.
(v) Write the complete equation y(x,t) of the wave.