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?

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