A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the wat

Question

A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.90 s for the boat to travel from its highest point to its lowest, a total distance of 0.700 m . The fisherman sees that the wave crests are spaced a horizontal distance of 5.50 m apart.

How fast are the waves traveling?

What is the amplitude A of each wave?

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Thu Nguyệt 3 days 2021-07-19T06:09:57+00:00 1 Answers 2 views 0

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    2021-07-19T06:10:59+00:00

    Answer:

    Velocity=1.1m/s

    Amplitude=0.35m

    Explanation:

    Given:

    time ‘t’ = 2.9s

    wavelength ‘λ’= 5.5m

    distance ‘d’=0.7m

    The time period ‘t’ is the time b/w two successive waves. Therefore, the time it takes from the boat to travel  from its highest point to its lowest is a half period.

    So, T = 2 x 2.9 => 5.8 s

    As we know that frequency is the reciprocal of time period, we have

    f= 1/T = 1/5.8 =>0.2 Hz

    In order to find how fast are the waves traveling, the velocity is given by

    Velocity = f λ

    V= 0.2 x 5.5 =>1.1m/s

    The distance between the boat’s highest point to its lowest point is double the amplitude.

    Therefore , we can write

    Amplitude ‘A’= d/2 =>0.7/2 =>0.35m

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