Starting with a diagram and fundmantal definitions and/or principles, show how the propagation of a wave pulse can be understood/modeled as a phase-staggered collection of identical oscillators. The more steps and explanation you include, the more thorough and clear your analysis,

The energy of a ripple on a pond is proportional to the amplitude squared. If the amplitude of the ripple is 0.1 cm at a distance from the source of 6.00 meters, what was the amplitude at a distance of 2.00 meters from the source?

(a) Seismographs measure the arrival times of earthquakes with a precision of 0.100 s. To get the distance to the epicenter of the quake, geologists compare the arrival times of S- and P-waves, which travel at different speeds. If S- and P-waves travel at 4.00 and 7.20 km/s, respectively, in the region considered, how precisely can the distance to the source of the earthquake be determined? (b) Seismic waves from underground detonations of nuclear bombs can be used to locate the test site and detect violations of test bans. Discuss whether your answer to (a) implies a serious limit to such detection. (Note also that the uncertainty is greater if there is an uncertainty in the propagation speeds of the S- and P-waves.)

Consider the superposition of three wave functions y(x,t)=3.00cmsin(2m1x3s1t) , y(x,t)=3.00cmsin(6m1x+3s1t) , and y(x,t)=3.00cmsin(2m1x4s1t) . What is the height of the resulting wave at position x=3.00 m at time t=10.0 s?