(1)

"One very good way of locating fish and ships is active sonar, which involves sending out sound and listening to the echo. Whales, however, appear to hate the sound signals that are sent out. It confuses them and disrupts their behaviour; they have even been known to beach themselves to avoid the sound.

The answer is, not to send sound out into the ocean[.]"

(2)

"[B]ut first we need to establish the depth of the ocean in the vicinity of the ship. This can be done using active sonar: send a pulse of sound directly downwards and listen for its echo."

I don't suppose the world will stop sending sound out into the ocean, as suggested in (1) (as much as we might wish) so I appreciate very much the use of mathematics to try and reduce the silencing of whales from one another that we cause.

However, I wonder if this does not simply mean whales are more likely to get a concentrated blast if they are more directly below us? That is a genuine question. I do not know anything about how sonar propagates in water. Does firing straight down reduce the total area affected by our sonar?

Thanks for this article and your work to help us humans be a little less awful to other creatures who share the planet with us.