A research vessel deploys three instruments to study energy transmission beneath the ocean surface:
• Instrument A releases a burst of visible light that must travel 500 m through seawater to a photodetector.
• Instrument B generates a sharp underwater acoustic pulse that travels the same 500 m to a hydrophone.
• Instrument C produces a mechanical surface wave that propagates 500 m along a taut, 2-cm-diameter steel cable connecting the vessel to a remote buoy.
Relevant data:
• Speed of light in seawater: 2.3×108m/s
• Speed of sound in seawater: 1.5×103m/s
• Speed of transverse waves on the cable: 7.0×103m/s
Neglect any dispersion or attenuation effects that are not explicitly requested.
(a) Calculate the travel time for each of the three signals to cover the 500 m path. Present your results in scientific notation with appropriate units.
(b) Rank the three signals in order of arrival at the detector from fastest to slowest. Justify your ranking in terms of fundamental wave properties.
(c) Discuss one practical engineering challenge unique to each instrument that arises from the nature of the wave it emits.
(d) Suppose the acoustic pulse amplitude is doubled while the light and cable-wave amplitudes remain unchanged. Describe qualitatively how this change affects the energy transported by the acoustic pulse and compare it with any analogous change that would occur for the light signal.