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Numericals · Q28

Q.An echo-sounder in a fishing boat receives an echo from a shoal of fish 0.45 s after it was sent. If the speed of sound in water is 1500 m/s, how deep is the shoal?

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The echo-sounder's pulse travels DOWN to the shoal of fish and back UP to the boat, so the 0.45 s recorded is the ROUND-TRIP time for a total distance of 2×depth2\times\text{depth}. With speed of sound in water v=1500v=1500 m/s: total distance =v×t=1500×0.45=675=v\times t=1500\times0.45=675 m. This is twice the depth, so depth =6752=337.5=\dfrac{675}{2}=337.5 m. [!ANSWER] Depth of the shoal = 337.5 m

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