Waves are produced in a medium from two sources. Each source can produce the sinusoidal tr...

Waves are produced in a medium from two sources. Each source can produce the sinusoidal travelling waves A, B, or C as shown in Figure P12.72i. If both sources are turned on at the same time, interference will occur and produce a combined wave pattern, (a) Using the principle of superposition, construct the shape of the wave that is formed by producing the waves A and B in the medium at the same time. Hint: Construct (sketch) the new wave A + B by considering small steps in the x direction and adding the displacements from the vertical as shown in Figure P12.72ii for each increment, (b) Construct the wave produced if waves A and C are applied simultaneously, (c) Find the wave produced by the combination of waves B and C. (d) If the grid lines denote intervals of 10 cm in x and 1.0 cm in y, what is the wavelength for waves A, B and C? (e) What are the wavelengths of the wave found in parts (a) through (c)? (f) When combining waves, is there always a final wavelength to measure?

Figure P12.72