Upon manifestation, Squeaks will gain the ability to emit ultrasonic clicks and squeaks with her voice that she can then use to create a mental ‘map’ of her surroundings. As is true of other creatures who’ve evolved echolocation, Squeaks will be able to instantly gauge distance, terrain, the presence of moving objects, etc by translating the echoes of the sounds she emits.
All her years underground and her time learning how and making physical maps has helped make her ability manifest even more precisely, allowing her to retain and store the information and use it more effectively. (And one might even wonder if her ability had been active for years to a lesser degree and she just didn't know it.)
This ability has three main forms. Creating the ultrasonic sounds, acute hearing, and mental mapping.
Emission of Ultrasonic Sounds
The calls Squeaks emits are somewhere within the range of 14-100kHz. These sounds can dip into the range of human hearing (under 20kHz), but mostly exist outside of regular human perception, and range from 60 to 90 decibels — similar in nature to the calls of the average echolocating bat. Generally, when using her active echolocation she would create 10-20 clicks or squeaks per second to gain an accurate, but somewhat broad strokes feel for the environment around her, with a lower resolution ‘image’ and a jerkier frame rate for perceiving movement.
She can increase the rate of sounds to quick succession for finer guidance (known as terminal buzz) for short periods of time (a few seconds) at rates as high as 200 clicks or squeaks per second before risking sensory overload. This ‘terminal buzz’ paints a much more precise, high definition image, and provides a much more detailed burst of information (more on this below).
Sensory overload will result in a brief sensory 'white out' where all of Squeaks' sensory perception is in danger of being jammed. Similar to standing up too quickly when everything goes white and fuzzy and rings with tinnitus — the lock up is brief but potentially very dangerous in a hostile situation.
In addition to flooding Squeaks’ senses, using this temporary boost also creates a quiet, rapidfire clicking that is audible to human ears.
Particularly at first, this sharp increase in frequency might be triggered by pain or adrenaline.
Enhanced Hearing
Squeaks is able to perceive ultrasonic sound in the range she’s capable of producing, with a natural tendency to focus in on her own clicks and squeaks. The rest is generally filtered out as white noise.
She can glean data from the squeaks of bats and other animals capable of using echolocation within her same range, but only in small glimpses for each ping — similar to trying to pick out details in a room with a very small strobing flashlight vs the floodlight of her usual capability.
At current, this specialized hearing does not extend past the distance range of regular human hearing — she doesn’t have the brand of super hearing that allows for her to hear very far away or quiet conversation, for example.
Mental Mapping
Echolocation all leads up to mental maps based on sound waves and the interpretation of them. Her range depends a lot on the area that she's utilizing the ability as well as the squeaks per second mentioned above in emission.
The slower the pulses (squeaks per second), the larger the area she can sense and get a basic idea. The faster the pulses the shorter the range and more finite and focused the mental map.
At the lowest example (10-20 squeaks per second), she can detect objects and obstacles within 60 feet and create a crude map of the area. At quicker, terminal buzz succession, she can focus her bursts to a smaller area (10 feet) and get more minute details, even details that the normal human eye would miss (physical weaknesses in structures, fine texture detail), even if in absolute darkness.
Enclosed areas, like caves and sewers and rooms tend to be more detailed than wide open areas, but she can still utilize the ability in the woods or in the city streets. The image just tends to be less precise (and sometimes less accurate) due to sound loss, distraction and interference from the environment.
The images created by this ability are three-dimensional renderings of the surrounding space and objects within it — perceived similarly to vision without color or light to cast shadows. Instead, objects (especially large objects) might cast echo shadows that she'll have to bounce clicks around to see behind. You'll have some flexibility to decide how Squeaks perceives this rendering, but ultrasound imagery and sonar are good points of reference. As a basic rule, she can 'see' space, distance, dimensions and movement, but not light, temperature or color. Texture and density information is something reserved for rapid click bursts, and even then limited to her understanding of how different materials bounce back sound (distinguishing metal from flesh or cardboard, for example). This is something she could probably get better with by practicing and honing her skills over time.