A vehicle is fitted with an ultrasonic distance sensor as part of parking assistance system which provides echolocation, while the driver is reversing the vehicle. It emits ultrasonic wave (about 40 kHz) which is reflected by the obstacle. When the warning beep starts sounding at a distance of 1.2 m from the obstacle, how much time is taken by ultrasonic wave to travel to the obstacle and come back? Assume the speed of ultrasonic wave in air to be 345 m s⁻¹.
0.00696 s
Explanation
The ultrasonic wave travels from the sensor to the obstacle and then reflects back to the sensor. Therefore, the total distance covered by the wave is twice the distance between the vehicle and the obstacle. By rearranging the standard echo formula (distance = speed × time / 2), we can find the total time taken for the round trip by dividing the total distance by the speed of the wave.
Solution Steps
Step 1: Identify the given values: Distance to the obstacle (d) = 1.2 m, Speed of ultrasonic wave (v) = 345 m s⁻¹.
Step 2: Calculate the total distance traveled by the ultrasonic wave. Since the wave travels to the obstacle and back, Total Distance = 2 × d = m = 2.4 m.
Step 3: Apply the formula to find the time taken: Time = Total Distance / Speed.
Step 4: Substitute the values into the formula: Time = 2.4 m / 345 m s⁻¹ 0.00696 s.