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A pendulum has a frequency of 4 vibrations per second. An observer starts the pendulum and fires a gun simultaneously. He hears the echo from the cliff after 6 vibrations of the pendulum. If the velocity of sound in air is 340 m s-1, find the distance between the cliff and the observer.

Work, Energy & Power

ICSE 2019

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Answer

Echo is heard after 6 vibrations of pendulum. Since frequency of pendulum is 4 vib per sec, so the time taken for the echo to be heard is t = 64\dfrac{6}{4} = 1.5 s.

If d is the distance between the cliff and the observer, then velocity of sound V = 2dt\dfrac{2d}{t}

Substituting the values in the equation above:

340=2d1.5d=340×1.52=255 cm340 = \dfrac{2d}{1.5} \\[0.5em] \Rightarrow d = \dfrac{340 \times 1.5}{2} = 255 \text{ cm}

Hence, distance between the cliff and the observer = 255 cm

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