An ultrasonic rangefinder mounted on a drone sends a sound pulse vertically downward to me… — JAMB UTME

An ultrasonic rangefinder mounted on a drone sends a sound pulse vertically downward to measure its altitude above flat ground. If the echo is detected by the sensor $0.08\text{ s}$ after emission and the speed of sound in air is $340\text{ m s}^{-1}$ , what is the altitude of the drone in meters?

Answer: 13.6 m

Answer

13.6 meters

The sound pulse emitted by the drone travels down to the ground and reflects back to the sensor. The relationship between speed

v

, total round-trip time

t

, and altitude

d

is given by

2d = v \times t

. Substituting

v = 340\text{ m s}^{-1}

and

t = 0.08\text{ s}

yields

d = \frac{340 \times 0.08}{2} = 13.6\text{ m}

Step-by-Step Solution

Identify the total time taken by the sound pulse for the round trip.

Total round-trip time

t = 0.08\text{ s}

and speed of sound

v = 340\text{ m s}^{-1}

Echo detection measures the time for sound to travel to a barrier and return.

Apply the echo distance relationship

2d = v \times t

to solve for altitude

d

d = \frac{340 \times 0.08}{2} = 13.6\text{ m}

Dividing the total path distance by 2 yields the one-way distance to the ground.

Key Concept

Calculation of distance using echoes and two-way sound wave propagation

Alternative Method

Determine the one-way travel time first:

t_{\text{one-way}} = \frac{0.08}{2} = 0.04\text{ s}

. Then calculate altitude directly using distance = speed × one-way time:

d = 340 \times 0.04 = 13.6\text{ m}

Estimated Time:1m 0s

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