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Question

A swimming duck paddles the water with its feet once every 1.6s, producing surface waves with this time period. The duck is moving at constant speed in a pond where the speed of surface waves is 0.32m/s, and the crests of the waves ahead of the duck are spaced 0.12m apart, (a) what is the duck’s speed? (b) How far apart are the crests behind the duck?

A
0.245 m/s, 0.904 m
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B
0.350 m/s, 0.715 m
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C
0.44 m/s, 1.3 m
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D
0.12 m/s, 0.452 m
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Solution

The correct option is A 0.245 m/s, 0.904 m
(a) λ=0.12
Surface wae speed v = 0.32m/s
f=vλ=0.320.12=2.66 Hz
f=1T=11.6=0.625 Hz
Now using f=f(vvvs)
Here, vs=velocity of source or velocity of duck
2.66=0.625(0.320.32vs)
Solving we get vs=0.245 m/s

(b) Behind the duck
f=f(vvvs)=0.625(0.320.32+0.245)=0.354 Hz
λ=vf=0.320.354=0.904 m

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