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No, of course it is not limitless. It's actually not very far, just a few metres, especially at the higher frequencies the animal uses to home in on its prey.

The range depends not only on the species, but also on various factors including call frequency, the bat's calling power (very low) and the reflectivity of the target.

It is influenced by the loudness of the call which in some species can well exceed 100dB re 20µPa. (That 20 micro-pascals is used as the reference sound-pressure level for airborne sound in decibels, as it is that of the quietest sound humanly audible within the human frequency range and so = 0dB). Even so the bat is a very small creature so its call power is very low.

As frequency rises so transmission range falls. Some of the power is lost by the beam-width - i.e. some of the sound misses the target by spreading out. (I wonder if the fungal infection, White Nose Syndrome, presently devastating the American bats is particularly serious among the horseshoe bats? Their peculiar nose-leaves focus the call - damage to the leaf may damage its sound beam-forming ability so reduce the echo-locating efficiency & accuracy.)

The theoretical minimum attenuation with distance is an inverse-square law, and since the bat is relying on the echo, the sound has to travel to the target then return, so that's two distance-squared losses.

Let's do the sums: 100dB call sound pressure level 1 metre from the animal's face is reduced by [20 log1010] dB at 10m away, so 20dB loss. If the sound hits a flat, fully acoustically-reflective surface it will therefore start its return at 80dB, so reach the bat's ears at 60dB (ignoring the approaching animal's slight change of position in the meantime). A loss overall of 40dB. And that's the theoretical maximum, ignoring all other sources of loss. The reality is far lower.

For one thing, the sound is extremely unlikely to fall on a perfectly reflective surface, so a good deal of its energy is either absorbed or bounced off at angles away from the bat. The bat's brain also has to sift the distorted echo of its own voice from a solid object or its prey from all the specular reflections from the surrounding objects.

So whilst it's impossible to give clear ranges for bats generally, it is normally little more than perhaps 10 metres, especially for the hunting chirps which are according to species but might sweep from about 80kHz up to about 140kHz. For more general navigation, and for "social" calls, bats use lower-frequency squeaks that will travel further than at high frequencies.

A great deal of research has been done, and continues to be done on bat's echo-location; even to the extent of using models of bat's heads to trace the acoustics.

As for what they "see", we can only speculate. Flying at dusk in the open air they have their eyes to help them, but navigating in absolute darkness in caves and tunnels requires 100% echo-location plus excellent homing and direction instincts, and it's surprising how far into caves they will fly, even through quite small, zig-zagging passages.

We can't tell what image the animal's brain forms from the echoes; we can only marvel at the incredible depth and speed of signal-processing going on in a small part of a brain weighing just few grammes in all. It is using the echo-data at perhaps 10 pulses/second, and other senses' returns, not only to "see" its world but also to synchronise the flight, breathing, calling, ear-damping and jaws... while the rest of the brain continues monitoring and operating the rest of the animal generally.

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