At a certain instant the shape of a sinusoidal wave travelling on a stretched string is examined and its profile is found to be perfectly periodic along the x-axis. The successive crests are seen at x = 12 cm, 32 cm, 52 cm, … while the maximum displacement of the string from the equilibrium line is 3.0 cm.
Answer the following with clear reasoning and suitable sketches where asked.
(i) Explain how the wavelength and the amplitude of the wave are obtained from the above spatial profile. State their numerical values.
(ii) If on your graph paper the distance between x = 12 cm and x = 32 cm is represented by 8.0 cm, determine the scale (cm on graph paper per centimetre in the actual string) used for the x-axis.
(iii) A second wave on the same string has the same amplitude but half the wavelength of the first. Describe qualitatively how the spacing of its crests would appear on the same scale.