Please show work for prompt ratings! A small ball floats in the center of a circ
ID: 1949904 • Letter: P
Question
Please show work for prompt ratings!
A small ball floats in the center of a circular pool that has a radius of 5.00 m. Three wave generators are placed at the edge of the pool, separated by 120.degree. The first wave generator operates at a frequency of 2.00 Hz. The second wave generator operates at a frequency of 3.00 Hz. The third wave generator operates at a frequency of 4.00 Hz. If the speed of each water wave is 5.00 m/s, and the amplitude of the waves is the same, sketch the height of the ball as a function ol time from t = 0 to t = 2.00 s, assuming that the water surface is at zero height. Assume that all the wave generators impart a phase shift of zero. How would your answer change it one of the wave generators was moved to a different location at the edge of the pool?Explanation / Answer
Amplitude = wavelength*2?(# of waves) ***1Hz = 1 s^(-1)*** wavelength 1)5m/s / (2Hz) = 2.5 m 2)5m/s / (3Hz) = 1.667 m 3)5m/s / (4Hz) = 1.25 m # of waves 1) 2Hz * 2s = 4waves 1) 3Hz * 2s = 6waves 1) 4Hz * 2s = 8waves individual amplitudes 1) amplitude = 2.5m*2/4 waves = 1.25 m 2) amplitude = 1.67m*2/6 waves = .556 m 3) amplitude = 1.25m*2/8 waves = .156 m Total amplitude: .156 m+1.25 m+.556 m=1.962 m If one of the generators were moved, the ball will not go up as high because the waves arent classing exactly against each other. Thus the amplitude will be less and also the ball will move to one direction. (since the waves arent perfectly cancelling out) Hope that helps! :)