Calculate the distance covered by the Ultrasonic wave having a velocity of 1.5 kms-1 in 14 s, when it is received after reflection by the receiver of the SONAR.
Topic: SONAR
Answer
Given: velocity of the ultrasonic wave v = 1.5 km s⁻¹, total time t = 14 s
The wave travels from the SONAR to the seabed and back, so the 14 s covers the whole round trip: total distance = v × t = 1.5 × 14 = 21 km
The distance of the object from the SONAR is half of that: d = 21 ÷ 2 = 10.5 km
Distance of the object from the SONAR = 10.5 km (the wave itself covers 21 km in all).
Be clear which quantity is wanted. The wave TRAVELS 21 km altogether; the object is 10.5 km away, because half that path is the outward journey and half the return. Write both lines and you cannot be marked down either way.
The speed is in km s⁻¹ and the answer is asked for in kilometres, so no conversion is needed here — but check the units every time, because SONAR questions often give the speed in m s⁻¹ instead.
The same 2d = vt relation covers echoes in air, radar and SONAR alike.