Electromagnetic earthquake precursor. A group of Stanford scientists measured75 mysterious electromagnetic waves varying with ultralow frequencies in the range of 0.01-10 Hz during two different earthquakes which occurred in Santa Cruz, California, in 1989 and in Park field, California, in 1994. A member of the group speculates that these waves may result from a local disturbance in the earth's magnetic field caused by charged particles carried by water streams that flow along the fault lines deep in the earth's crust as a result of the shifts that led to the quake. These low-frequency waves can penetrate rock much more easily than those of higher frequencies but can still travel only about 15 km through the ground. Since this low-frequency electromagnetic activity was recorded close to a month before the quake and lasted about a month after, this phenomenon has a potential use as an earthquake predictor. Consider three plane waves of equal amplitudes with frequencies of 0.1 Hz, 1 Hz, and 10 Hz, all produced at a depth of 15 km below the earth's surface during an earthquake. Assuming each of these waves to be propagating vertically up toward the surface of the earth, (a) calculate the percentage time-average power of each wave that reaches the surface of the earth and (b) using the results of part (a), comment on which one of the three signals is more likely to be picked up by a receiver located on the earth's surface, based on their signal strengths. For simplicity, assume the earth's crust to be homogeneous, isotropic, and nonmagnetic with properties respectively.