Question

The mathematical model for a wave on a tightly stretched wire Is tx, )-0.340 sin( 12nt 3x _ where x and y are in meters, t is in seconds, and μ of the wire is 78.0 g/m. (a) Calculate the average rate energy is conveyed along the wire (in W) Apply the equation for the power of a wave. You will need to calculate v. Recall the relationship among v, k, and u. From the given wave function, you can find k and ω If you recast the equation so that it is in standard form. You might find the identity sin(A)n( A) helpful. W (b) What Is the energy per cycle of the wave (In J)? Need Help? Read It Submit Answer Save Progress Practice Another Version

Answer 1

Concept: we use the expression for average power for wave on a string and then find the time period which is the time for one cycle and the use relation between power and energy to find the energy in one cycle

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Concept: we use the expression for average power for wave on a string and then find the time period which is the time for one cycle and the use relation between power and energy to find the energy in one cycle a) P_avg = 2 pi^2 mu vA^2 f^2 mu = 78 times 10^-3 kg/m f = omega/2 pi = 12 pi/2 pi = 6 Hz A = 0.34 m v = omega/k = 12 pi/3 pi = 4 m/s So, P_avg = 25.63 W b) time for one cycle = T = 2 pi/omega = 2 pi/12 pi = 1/6 s So, E = (P_avg)T = (25.63 W)(1/6)s = 4.27 J