Emit sounds from the microphone and measure how long they take to return. There are some apps out there that do this already, such as PocketMeter. I suspect this would not be user friendly, and more gimmicky than practical.
Au contraire, mon frère.
This is the most user friendly, not to mention accurate, way of measuring the dimensions of a room.
PocketMeter measures the distance to one wall with an accuracy of half an inch.
If you use the same formulas to measure distance, but have the person stand near a corner of the room (so that the distances to the walls, floor, and ceiling are all different), you should be able to calculate all three measurements (length, width, and height) with one sonar pulse.
Edited, because of the comment, to add:
In an ideal world, you would get 6 pulses, one from each of the surfaces. However, we don't live in an ideal world. Here are some things you'll have to take into account:
- The sound pulse causes the iPhone to vibrate. The iPhone microphone picks up this vibration.
- The type of floor (carpet, wood, tile) will affect the time that the sound travels to the floor and back to the device.
- The sound reflects of off more than one surface (wall) and returns to the iPhone.
If I had to guess, because I've done something similar in the past, you're going to have to emit a multi-frequency tone, made up of a low frequency, a medium frequency, and a high frequency. You'll have to perform a fast Fourier Transform on the sound wave you receive to pick out the frequencies that you transmitted.
Now, I don't want to discourage you. The calculations can be done. However, it's going to take some work. After all PocketMeter has been at it for a while, and they only measure the distance to one wall.