This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Identify the given information. The problem states that the period of the wave is T = 0.5 \, s. The graph shows displacement versus what appears to be distance, despite being labeled as a "displacement-time graph". For a wave velocity calculation, we need both period (or frequency) and wavelength. Given the x-axis labels (10, 20, 30, etc.) and the y-axis in cm, it is standard practice to interpret the x-axis as distance in cm to extract the wavelength. Step 2: Determine the wavelength () from the graph. A complete wave cycle (one wavelength) is the distance over which the wave's shape repeats. From the graph, one full wave cycle starts at 0, goes up to a crest, down through the equilibrium to a trough, and back to the equilibrium position. This cycle completes at the x-axis value of 20. Therefore, the wavelength = 20 \, cm. Step 3: Convert the wavelength to meters. Since 1 \, m = 100 \, cm: = 20 \, cm = 20 × 10^-2 \, m = 0.20 \, m Step 4: Calculate the velocity of the wave. The velocity of a wave (v) is given by the formula: v = ()/(T) Substitute the values of and T: v = 0.20 \, m0.5 \, s v = 0.4 \, m/s The velocity of the wave is 0.4 m/s.