Physics
Physics
Problem
Oceanographers employ microwave radar pulses to measure the distance to the sea floor. In seawater, electromagnetic waves propagate at an effective speed that is times their speed in a vacuum. A radar system onboard a research vessel emits pulses at a frequency of (gigahertz). For the purposes of this problem, neglect any absorption or scattering losses. (a) Calculate the wavelength of the radar pulses in seawater. (b) If the vessel is directly above a point on the sea floor whose depth is , determine the round-trip travel time (emission to return) for a radar pulse. (c) To improve depth resolution, engineers propose doubling the radar frequency while all other system parameters remain unchanged. Predict quantitatively how the wavelength in seawater and the round-trip travel time would be affected. Provide numerical values and explain your reasoning.Intuitive explanation
This problem combines wave properties with distance measurement using the radar principle: a pulse travels down to the seafloor and back up, so you need to account for the round trip. The key insight is that the wave's speed in seawater is reduced compared to vacuum, which changes its wavelength but not its frequency—the source frequency stays constant. Once you know the wave speed in the medium and the travel time (from the pulse delay), you can find the distance the pulse actually traveled.
Intuitive explanation
This problem combines wave properties with distance measurement using the radar principle: a pulse travels down to the seafloor and back up, so you need to account for the round trip. The key insight is that the wave's speed in seawater is reduced compared to vacuum, which changes its wavelength but not its frequency—the source frequency stays constant. Once you know the wave speed in the medium and the travel time (from the pulse delay), you can find the distance the pulse actually traveled.