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 ms⁻¹.

Given that:

Distance of obstacle from vehicle = 1.2 m

Speed of ultrasonic wave = 345 ms⁻¹

Since the ultrasonic wave travels to the obstacle and comes back, the total distance travelled is 2d:

$$2 \times 1.2 = 2.4 \text{ m}$$

We know that,

$$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$$

$$t = \frac{2.4}{345}$$

$$t \approx 0.00696 \text{ s}$$

$$t \approx 0.007 \text{ s}$$

Therefore, the ultrasonic wave takes approximately 0.007 s to travel to the obstacle and return back.