Underwater Acoustics and Sonar Quiz
Sound in the ocean obeys the same wave equation as sound in air, yet the medium transforms every practical parameter. Seawater carries acoustic energy roughly 4.3 times faster than air at 20 °C — near 1,480 m/s against 343 m/s — and its density of about 1,025 kg/m³ reshapes the impedance mismatch at every boundary.
This quiz tests the quantitative core of Lesson 25:
- The sound speed profile and the SOFAR channel
- Impedance, reflection and the sea surface as an acoustic mirror
- Sonar ranging, echo timing and active versus passive sonar
- Spherical versus cylindrical spreading losses
- Hydrophones, transducers, echolocation and underwater communication
Track your units and sign conventions carefully — JEE questions on echo timing and Doppler-corrected depth measurement reward precision over memorisation.
Q1. At 20 °C, the speed of sound in seawater is approximately 1,480 m/s while in air it is 343 m/s. The ratio of the speed in seawater to that in air is closest to:
Dividing 1,480 by 343 gives approximately 4.3, so seawater carries acoustic energy about 4.3 times faster than air at 20 °C.
Q2. The acoustic impedance of a medium is given by ##Z = \rho v##. Using ##\rho_{water} \approx 1025\ \text{kg/m}^3## and ##v \approx 1480\ \text{m/s}##, the acoustic impedance of seawater is closest to:
Multiplying density by speed: ##1025 \times 1480 \approx 1.5 \times 10^{6}\ \text{Pa·s/m}##, which exceeds the impedance of air (about 413 Pa·s/m) by roughly three orders of magnitude.
Q3. Because ##Z_{water} \approx 1.5 \times 10^{6}\ \text{Pa·s/m}## greatly exceeds ##Z_{air} \approx 413\ \text{Pa·s/m}##, what happens to sound striking the water–air interface from below?
The huge impedance contrast means the intensity reflection coefficient is close to unity, so the sea surface acts as a near-perfect acoustic mirror and a submerged source radiates poorly into the atmosphere.
Q4. In the upper ocean, temperature dominates the sound speed profile. As depth increases in this warm surface layer, the speed of sound generally:
In the upper ocean temperature falls with depth and dominates over pressure, so the sound speed decreases with depth. Pressure only takes over in the deep ocean.
Q5. The SOFAR channel forms near a depth of about 1,000 m because:
In the upper ocean temperature lowers the speed while in the deep ocean pressure raises it; between these regimes a minimum forms near 1,000 m, and refraction bends rays toward this slower layer.
Q6. Refraction of sound rays in the ocean follows Snell's law applied continuously. Along a ray, the quantity that stays constant is:
For rays measured at angle ##\theta## to the horizontal, the continuous form of Snell's law gives ##\dfrac{\cos\theta}{v} = \text{constant}##, so a ray curves back toward the slower layer.
Q7. A sonar pulse is sent downward and its echo returns after 2.0 s. Taking the speed of sound in seawater as 1,500 m/s, the depth of the reflecting object is:
The pulse travels to the object and back, so ##2d = vt = 1500 \times 2.0 = 3000\ \text{m}##, giving ##d = 1500\ \text{m}##.
Q8. Which statement correctly distinguishes active from passive sonar?
Active sonar transmits a pulse and times the returning echo to obtain range, whereas passive sonar merely listens to sound radiated by the target and does not reveal its own presence.
Q9. For a compact source radiating freely in the open ocean, spherical spreading reduces the intensity with distance ##r## as:
Spherical spreading distributes the same power over a sphere of area ##4\pi r^{2}##, so intensity falls as ##1/r^{2}##. Cylindrical spreading inside a channel falls only as ##1/r##.
Q10. A signal confined within the SOFAR channel suffers cylindrical spreading rather than spherical spreading. Compared with free-field spherical spreading, this channel confinement:
For cylindrical spreading, intensity falls as ##1/r##; for spherical spreading, it falls as ##1/r^{2}##. Setting ##I_0/r_c = I_0/r_s^{2}## for the same threshold gives ##r_c = r_s^{2}##, so the cylindrical-spreading range equals the square of the spherical-spreading range (in consistent units), not merely twice it.
Q11. A hydrophone is best described as:
A hydrophone is essentially an underwater microphone: it receives acoustic pressure variations and converts them into electrical signals for measurement or recording.
Q12. Marine mammals such as dolphins use echolocation. The physical principle underlying echolocation is essentially the same as that of:
Echolocation involves emitting a sound pulse and interpreting the returning echo to locate and characterise objects, which is the same principle as active sonar ranging.
Q13. Which of the following is a genuine challenge specific to underwater acoustic communication?
Boundary reflections, refraction in the sound speed profile and reverberation create multipath interference, which is a major practical challenge for underwater acoustic communication.
Q14. Side-scan sonar is primarily used to:
Side-scan sonar directs acoustic beams sideways to image and map the seafloor, revealing topography and objects on the bottom.
Q15. In the deep ocean below the sound channel, the sound speed rises with depth at roughly 0.017 m/s per metre. This rise is caused mainly by:
In the deep ocean temperature is nearly constant, so the dominant effect is hydrostatic pressure, which increases the bulk modulus and raises the sound speed with depth.