Final answer:
The correct expression for the range of an HC-SR04 ultrasonic sensing device, with a speed of sound at 350 m/s and echo time in microseconds, would be option (d): r = Speed × EchoTime / 2000.
Step-by-step explanation:
If the speed of sound is 350 m/s, and we want to find the expression for range r of an HC-SR04 ultrasonic ranging device in centimeters (cm) as a function of echo time, Techo in microseconds (us), we need to account for the conversion between meters and centimeters, and seconds to microseconds.
We know that:
Thus, we can convert the speed of sound into cm/us (350 m/s * 100 cm/m * 1 s/1,000,000 us = 0.035 cm/us).
The range, r, is effectively half the distance the sound wave travels since it goes to the object and comes back. Therefore, the formula to calculate the range would be:
r = (Speed of sound in cm/us) * (Techo in us) / 2
Upon inserting the values, we obtain:
r = 0.035 cm/us * Techo / 2
This simplifies to:
r = Techo * 0.0175 cm/us
Therefore, the correct expression for range r is:
d) r = Speed × EchoTime / 2000