The speed of sound is 343 meter/sec at 20 degrees Celsius. That is 34300 centimeters/sec.

That is 0,03434 cm/microsecond or 0,01352 inches/microsecond.

The sensor measures the distance from and to the object, so we have to divide this value by 2.

That gives us 0,01717 cm/microsecond or 0,006760 inches/microsecond.

distance = pulsewidth (µs) * 0,01717 cm/µs.

distance = pulsewidth (µs) * 0,006760 inches/µs.

Instead of dividing by 2 and then multiplying by 0,03434 some code (for centimeters) uses a division by 58,24 which is mathematically the same. This saves one floating point operation and makes the code much harder to understand.

Thus 0,0001657 is a value I cannot understand, just like you.