Question

A swimming duck paddles the water with its feet once every 1.6s, producing surface waves with this period. The duck is moving at constant a speed in a pond where the speed of surface waves is 0.32 m/s, and the erests of the waves ahead of the duck are spaced 0.12 m apart. The duck's speed is $245\times {10}^{-x}m$.Find x.

Answer 1

Given - $T=1.6s$ , speed of wave $v=0.32m/s$ ,

original frequency of wave , $n=1/T=1/1.6Hz$ ,

wavelength of wave ahead of duck = difference between two consecutive crests ,

${\lambda }^{\prime }=0.12m$

frequency of wave ahead of of the duck , $n^{\prime }=v/{\lambda }^{\prime }=0.32/0.12m$

the swimming duck is the source of wave , let its speed is $v_s$ , therefore , frequency of wave ahead of duck will be ,

$n^{\prime }=n\left(\frac{v}{v-v_s}\right)$ ,

or $0.32/0.12=\left(1/1.6\right)\left(\frac{0.32}{0.32-v_s}\right)$ ,

or $1.6/0.12=1/(0.32-v_s)$

or $0.32-v_s=0.075$

or $v_s=0.245m/s$