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19 May, 00:11

A swimming duck paddles the water with its feet once per time interval of 1.6 s, producing surface waves with this period. The duck is moving at constant speed in a pond where the speed of surface waves is 0.40 m/s, and the crests of the waves ahead of the duck have a spacing of 0.20 m.

Part A: What is the duck's speed?

Part B: How far apart are the crests behind the duck?

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  1. 19 May, 01:52
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    a. 0.275m/s

    b. 1.08m

    Explanation:

    Since the duck the paddle the water at an interval of 1.6sec, we can determine the frequency of the wave formed using the equation

    f=1/T

    Where T is the period.

    f=1/1.6

    f=0.625Hz.

    Also from the equation used in determining the speed of a wave

    V=fλ,

    v=0.625*0.2

    v=0.125m/s

    in the question it was stated that that the duck produce a wave moving at a speed of 0.40m/s.

    Hence the speed of the duck is

    v (duck) = 0.40-0.125

    v (duck) = 0.275m/s

    b. The distance between the crest behind the duck is the wavelength of the waves.

    To determine this, the wavelength is expressed as

    λ=v/f

    but the speed in this case is the speed of the duck and the surface wave, as this account for the wave speed behind the duck,

    Hence we have

    λ = (0.40+0.275) / 0.625

    λ=1.08m.

    The wavelength behind the duck is 1.08m
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