1.3 Describe and explain A periodic wave disturbance created by a sinusoidally vibrating source at one particular time is represented by the graph below. In a way, the graph is a snapshot of the wave. Your physics major friend claims that the function that follows describes this periodic wave disturbance at different positions x at different times t: 271' 27r y(t,w) Acos (?t 7:) where y is the disturbance at time t of the medium at position x (the distance from the source). First examine the function and decide whether it makes sense. How is the function similar to the mathematical function describing SHM? How is it different? Answer the following questions to test her claim. Note thatA is the amplitude of the wave, T is its period, and is its wavelength. x 1. Without looking at the equation, answer the following questions: At t = 0 and x = 0, a particular wave disturbance has a value 3/ = A cos 0 = A, which matches what we see in the gure above. At the same time (t = 0), what should the value of the disturbance be at one wavelength forward? What will it be at two wavelengths forward? Three wavelengths forward? Now compare your answers to the answers predicted by the function above. Does the function give you the desired value? Explain. 2. Without looking at the equation, answer the following questions: At , what should the value of the wave disturbance be at positions x = A/Z, 3A/2, 5A/2, and so forth? Now compare your answers to the answers predicted by the function above. Does the function give you the desired values? Explain. 3. At , what will the value of the wave disturbance be at positions 1: = A/4, 3/\\/4, 5A/4, and so forth? Does the equation give you the desired value? Explain. 4. At t = T what will the value of y be at positions and a: = 0, A/4, A/Z, 3/\\/4, and A? Does the equation give you the desired values? Explain. 5. Does the mathematical description seem appropriate based on your analysis? Explain