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Zorluk: OrtaSound Waves, Echoes, Pitch, Loudness, and Quality

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 s0.08\text{ s} after emission and the speed of sound in air is 340 m s−1340\text{ m s}^{-1}, what is the altitude of the drone in meters?

Cevap: 13.6 m

Cevap

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 vv, total round-trip time tt, and altitude dd is given by 2d=v×t2d = v \times t. Substituting v=340 m s−1v = 340\text{ m s}^{-1} and t=0.08 st = 0.08\text{ s} yields d=340×0.082=13.6 md = \frac{340 \times 0.08}{2} = 13.6\text{ m}.

Adım Adım Çözüm

1
Identify the total time taken by the sound pulse for the round trip.
Total round-trip time t=0.08 st = 0.08\text{ s} and speed of sound v=340 m s−1v = 340\text{ m s}^{-1}.
Echo detection measures the time for sound to travel to a barrier and return.
2
Apply the echo distance relationship 2d=v×t2d = v \times t to solve for altitude dd.
d=340×0.082=13.6 md = \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.

Anahtar Kavram

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

Alternatif Yöntem

Determine the one-way travel time first: tone-way=0.082=0.04 st_{\text{one-way}} = \frac{0.08}{2} = 0.04\text{ s}. Then calculate altitude directly using distance = speed × one-way time: d=340×0.04=13.6 md = 340 \times 0.04 = 13.6\text{ m}.
Tahmini Süre:1m 0s
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Sound Waves, Echoes, Pitch, Loudness, and Quality

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