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Question

A sound signal is simultaneously sent in air and water from a boat on a river. The echo of sound returned by the river bed is heard is 4 s, while the echo returned by the aeroplane is heard in 8 s. Find the distance between the aeroplane and the river bed.

[velocity of sound in air = 350 m/s, velocity of sound in water = 1500 m/s]

A
4.4 km
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B
6.4 km
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C
8.8 km
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D
13.4 km
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Solution

The correct option is A 4.4 km
If the distance of reflector from the source is d, then
Total distance travelled by the sound before reaching the detector 2d=vtd=vt2
where t is the time taken to receive the reflected sound.

From the data given in the question,

Distance travelled by the sound in air from source to the reflector,
d1=350×82=1400 m ......(1)

Distance travelled by the sound in water from source to reflector,
d2=1500×42=3000 m ........(2)

Seperation between the aeroplane and the river bed is given by d=d1+d2

From (1) and (2) we get,
d=3000+1400=4400 m or 4.4 km

Thus, option (a) is the correct answer.

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