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
• B. 0.350 m/s, 0.715 m
• C. 0.44 m/s, 1.3 m
• D. 0.12 m/s, 0.452 m

Answer 1

The correct option is A 0.245 m/s, 0.904 m

(a) $\lambda =0.12$
Surface wae speed v = 0.32m/s
$f^{\prime }=\frac{v}{\lambda }=\frac{0.32}{0.12}=2.66Hz$
$f=\frac{1}{T}=\frac{1}{1.6}=0.625Hz$
Now using $f^{\prime }=f\left(\frac{v}{v-v_s}\right)$
Here, $v_s$=velocity of source or velocity of duck
$\therefore 2.66=0.625\left(\frac{0.32}{0.32-v_s}\right)$
Solving we get $v_s=0.245m/s$

(b) Behind the duck
$f^{\prime }=f\left(\frac{v}{v-v_s}\right)=0.625\left(\frac{0.32}{0.32+0.245}\right)=0.354Hz$
$\lambda =\frac{v}{f^{\prime }}=\frac{0.32}{0.354}=0.904m$