A swimming duck paddles the water with its feet once every `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 `0.32 m//s` , and the crests of the waves ahead of the duck are spaced `0.12 m` apart. (a) What is the duck's speed? (b) How far apart are the crests behind the duck?

Answer

A, B, D

Explanation

(a) `lambda = 0.12`
Surface wave speed, `nu = 0.32 m/s`
`f' = (nu) /(lambda) = (0.32)/(0.12) = 2.66 H_(Z)`
`f = (1)/(T) = (1)/(1.6) = 0.625 H_(Z)`
Now, using `f' = f ((nu)/(nu - nu_(s)))`
Here, `nu_(s) =` velocity of source or velocity of duck
`:. 2.66 = 0.625 ((0.32)/(0.32 - nu_(s)))`
Solving we get, `nu_(s) = 0.245 m//s`
(b) Behind the duck
`f' = f(( nu ) / (nu + nu_(s)))`
`= 0.625 (( 0.32)/(0.32 + 0.245))`
`= 0.354 H_(Z)`
`lambda = (nu) / (f') = (0.32)/(0.354) = 0.904 m`