Exercise 10.11
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 kHz) which is reflected by the obstacle. When the warning beep starts sounding at a distance of 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 m .
NCERT’s answer
0.$\displaystyle 007$ s
About \(\displaystyle 0.007\ \text{s} \).
The pulse goes to the obstacle and comes back, so the path length is \(\displaystyle 2 \times 1.2\ \text{m} = 2.4\ \text{m} \).
\(\displaystyle t = \dfrac{\text{distance}}{\text{speed}} = \dfrac{2.4\ \text{m}}{345\ \text{m s}^{-1}} = 0.00696\ \text{s} \approx 0.007\ \text{s} \).
The $\displaystyle 40$ kHz is not needed for the time — it only tells you the wave is ultrasonic (above $\displaystyle 20$ kHz), so the driver never hears the pulse itself, only the warning beep the system produces.