A research vessel sends an acoustic pulse of single frequency 25.0kHz into the ocean to map the sea floor. The speed of sound in seawater is taken as 1.50×103m s−1. The vessel detects the first strong echo exactly 2.40s after the pulse is emitted.
(a) Compute the one-way distance from the vessel to the reflecting point on the sea floor.
(b) Determine the wavelength of the emitted sound in seawater.
(c) Calculate the total number of complete wavelengths contained in the round-trip path of the pulse between emission and detection.
(d) Suppose the vessel were moving directly toward the reflecting point at a steady speed of 8.0m s−1. Without performing a full Doppler derivation, discuss qualitatively whether the number of wavelengths you calculated in part (c) would increase, decrease, or remain the same, and justify your answer using logical reasoning about the motion of the vessel relative to the medium.