In a laboratory investigation of transverse waves on a long rope, the following observations are made:
• A photograph shows that the distance from a chosen crest to the third crest ahead of it is 0.75 m.
• A displacement–time trace at a fixed point on the rope records 8 complete oscillations in 0.50 s.
• By tracking a marked crest with a high-speed camera, the wave speed is directly measured as 3.8 m s−1.
(i) Determine the wavelength of the wave from the photograph.
(ii) Determine the frequency of the wave from the time trace.
(iii) Using your answers to (i) and (ii), calculate the theoretical value of the wave speed.
(iv) Compare the theoretical speed with the directly measured value and state, with proper reasoning, whether the two results are consistent within 5 %.