A research boat moves due south across a calm lake at 8m⋅s−1 while continuously sounding a sonar "ping" at rest frequency f0. Three submerged probes record the sound:
• Probe H is directly beneath the boat at a depth of 10m and drifts due east with the gentle current at 0.5m⋅s−1.
• Probe I is 30m south of the boat’s current position, anchored to the lakebed.
• Probe J is 30m north of the boat’s current position, being pulled northward by a cable at 2m⋅s−1.
Neglect water movement other than the stated probe motions.
(a) Determine qualitatively which probe records the highest frequency and which records the lowest frequency at this instant. Explain your reasoning in terms of relative velocity components along the line connecting each probe to the boat.
(b) Two minutes later, the boat has continued south at the same speed. Without performing numerical calculations, discuss how the observed frequency at each probe has changed compared with part (a). Provide a separate qualitative explanation for each probe.
(c) During the interval, the boat’s captain briefly considered accelerating the boat to double its speed. Explain qualitatively how that change would have affected the ordering of frequencies in part (a), if at all.