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10 August, 07:59

A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.9 s after shouting. The speed of sound in air is 343 m/s. Determine the length of the lake.

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  1. 10 August, 08:48
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    497.35 m.

    Explanation:

    Echo: This is the sound heard after the reflection of sound wave on a plane surface.

    v = 2x/t ... Equation 1

    Where v = speed of sound in air, x = length of the lake, t = time taken to hear the echo.

    Making x the subject of the equation,

    x = vt/2 ... Equation 2

    Given: v = 343 m/s, t = 2.9 s.

    Substitute into equation 2

    x = 343*2.9/2

    x = 497.35 m

    Thus the length of the lake = 497.35 m.
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