Surely not.

The submarine with the larger more sensitive instruments in a quieter environment ought to be able to detect sound levels below that which their active opposition can.

If X amount of noise-energy hits the submarine, it only reflects Y<X of that energy, and only Z<Y of that reflection goes in the right direction to be detected by the opposition. The noise should be louder at the submarine, than at the thing detecting the submarine.

Both of these weigh in favor of the submarine detecting the searcher before the searcher detects the submarine.

The path loss for active sonar is, logarithmically, twice the path loss for passive sonar. If the signal is 0 dB at 1 meter, it will be -40 dB at 10 km away (barring SOFAR, a regions these submarines probably try to avoid, and ignoring the reflections off the surface and seafloor), and the reflection (assuming an isotropic reflector) will be -80 dB. At 100 km, it's -50 dB and -100 dB.

So, if both sides can detect a -50 dB signal, the passive-sonar target will be able to detect the active-sonar probe 100 km away, while the active-sonar target will be able to detect the reflection from the passive-sonar reflector 0.316 km away. Or maybe 0.315. And that's assuming perfect discrimination.

(By transmitting a signal you can barely detect, you can reduce this discrepancy: if you reduce the signal amplitude by 30 dB at 1 m in this example, the probe can detect the target at 10 m, or maybe 11 m, but the target can't detect it until they're within 100 m.)

However, this massive advantage for passive sonar only really true if it's just as easy for the target to recognize the signal as it is for the probe. In fact, the probe has a huge advantage: it knows what the signal was. If it's just an ordinary chirp, this is of no help, because that's easy to recognize, unless you confuse it for a humpback whale song or something. But if it's Gaussian white noise, it's impossible for a single hydrophone to distinguish from the background noise of the ocean, except by amplitude. Advantage: probe.

But that's a single hydrophone. In fact, though, a point source of white noise is the easiest thing for a phased-array beamforming passive-sonar system to localize. The Triomphant is 138 m long, so if you stuck hydrophones all along its length, you could detect directional sources of sound with an angular precision of about λ/d, the one-dimensional Airy limit. The λ for your active sonar needs to be chosen to be small with respect to the targets you're looking at so it doesn't just diffract around them, so this is probably on the order of 0.1 radians, about 5 degrees.

Two can play that game, though, or thousands. The network of tiny drones can form a single ocean-sized phased array by squirting data back and forth over short-range ultrasound or laser links.

But guess who already has ocean-sized phased arrays of hydrophones for passive sonar?

sca4 posted this very worthwhile link, which talks a bit more about the scene: https://www.aspistrategist.org.au/prospects-for-game-changer...