Great video from US Sub...didn't go into details regarding Thermocline layer & shadow zones in oceans & how to hide subs there or to detect them there.
Sound propagation work differently underwater & specially under ocean where Pressure, temperature, salinity, background noise both biological as well as human made will affect dB levels significantly. ambient noise of ocean range from around 55 dB to 105 dB.
Here's a chart from internet about Russian subs sound level relative to 1 Pa at 1 Mt at 5-200 Hz & 1kz frequency spectrum
Only speed of Sub are mentioned running at 4 to 8 knots ( 2 m/s to 4 m/s )
" ultra quite mode " ( i might me wrong so feel free to correct me )
If we go by dB level of old Soviet subs mentioned... well they were underwater orchestra but that doesn't tell the whole picture.
Sound dB level are different in underwater from air due to difference in reference measurement...this difference is about 62 dB if u calculate but will change further in ocean due to factor mentioned above ( depth, temperature, salinity, Thermocline layer etc )....so a Sub like Akula with 110 dB noise level at 1kz underwater at 4 to 8 knots won't be the same as in Air.
SlL ( Sound intensity level in Air ) = SIL ( Water ) - 62 dB
For Akula ( Sub closest to Arihant which India has Operated ) that turn out to be around 48 dB at 20 Pa at 1 mt in Air at 1kz which is very quite by the way...Its the same sound a house refrigerator make & 30dB at 5 to 200 Hz frequency spectrum which is same as whispering
u can than use sound attenuation formula to calculate the distance at which these sub can than be detected , which again will depend on the capabilities of the passive Sonar & as mentioned above there are shadow zones in oceans where this s**t doesnt work.
Loudest Sub ever recorded were Chinese Sub i think with upward of 170 dB ( real underwater orchestra )
Modern US & western subs have noise level lower than ambient noise of ocean.
They will pass just 1 meter away from u in ultra quite mode & u probably won't even hear them.
Russians have made great strides in their subs lately thanks to espionage.....but still not close to western subs. Western subs are smaller ( length & width wise ) & has much powerful Nuclear reactor & yet still more quite than the best Russian sub out there.
So how does that affect india ? well it does & it doesn't.
It does in a sense if Russians are so far behind west than how far indian is...our technology rely heavily on Russians
& it doesn't in a sense that our weapons are mostly geared toward Pakistan which doesn't have any capability. India for all purpose will remain a regional player & our Vishavguru dream will remain that just a pipe dream......far away from ground realities if we don't change our course.
India should look for west US or France for inspiration when setting parameters for designing a submarine specially nuclear subs & not russians going forward.