How does the transducer know how deep the water is?

Echo sounders measure the time between sending a sound and receiving its echo.

Sound travels through water at about 1,463 m/s (4,800 ft/s), which is less than a mile per second. To calculate the distance to an object, an echo sounder multiplies the time elapsed between the transmission of sound and the echo received by the speed of sound through the water.

The echo sounder system interprets the results and displays the water depth to the user.

How does the transducer know what the bottom looks like?

All sound waves travel at the same speed. When a sound wave in one part of the sound field returns faster than another, it is because the sound wave has bounced off closer to the transducer. The resulting images show all the bumps and bumps underwater.