Step 1: A sonar pings at f = 10 kHz in seawater (c = 1500 m/s). The echo from a submarine returns after 4.0 s. Find the range and the wavelength. Step 2: Range R = c·t/2 = 1500 × 4.0/2 = 3000 m = 3.0 km. Step 3: λ = c/f = 1500/10000 = 0.15 m = 15 cm. Step 4: Transmission loss (spherical spreading): TL = 20log₁₀(3000) = 20 × 3.477 = 69.5 dB one-way; the echo suffers it twice (~139 dB) plus absorption. Step 5: If the sub moves toward the sonar at 5 m/s, echo Doppler shift Δf = 2vf/c = 2×5×10000/1500 = 66.7 Hz — detectable, revealing motion. Result: 3.0 km range, 15 cm wavelength, ~67 Hz Doppler shift. Sonar turns time delay into distance.