Maths-Echolocation | Page 2

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THE OCEAN

By doing this sum – a subtraction with a multiplication – we get zero, i. e. we neutralise the fish scatter. Result: we make the fish invisible.

However, this isn’ t what we want. We want to make the bubbles invisible, not the fish.

The scatter from bubbles is stronger than from the fish. Bubbles change shape and expand and contract, so they bounce pulses back with more force. Let’ s say the bubbles magnify echoes as the square of the amplitude.( To square a number, you just multiply it by itself. We write it with a little 2 after the number being squared).

So, using the same subtraction with a multiplication as above: 12-( 3 x( 1 / 3) 2) = 1-( 3 x 1 / 9) = 1- 1 / 3 = 2 / 3 This is no good, either – we now know where the bubbles are, but the fish are invisible.

Method 2 – addition

What happens if we add the figures, rather than subtracting them?

This time, with the fish scatter, we get: 1 +( 3 x 1 / 3) = 1 + 1 = 2 The scatter is strong from the fish – we can‘ see’ them! What about the bubbles? From them, we get: 12 +( 3 x( 1 / 3) 2) = 1 +( 3 x 1 / 9) = 1 + 1 / 3 = 11 / 3

So, while we can‘ see’ the bubbles too, the scatter from them isn’ t as strong as from the fish. The fish are more visible than the bubbles. Result: Dolphins 1 – Fish 0!

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