Easy/fustrating doppler queston - rather

[hadroneater]

Easy/fustrating doppler question - rather urgent

Homework Statement

A swimming duck paddles the water with its feet once per time interval of 1.4 , producing surface waves with this period. The duck is moving at constant speed in a pond where the speed of surface waves is 0.31 , and the crests of the waves ahead of the duck have a spacing of 0.20 .

a)What is the duck's speed?
b)How far apart are the crests behind the duck?

Homework Equations

f_d = f_s (v + v_d)/(v + v_s)

The Attempt at a Solution

There are two things that I don't get. Is the duck the source or the detector of the waves? I think the duck is the source. Then f_s = 1/1.4 = 0.7142Hz
The waves in the front will have f_d = 0.31/0.2 = 1.55Hz and v_d = 0.31m/s
But what is the regular speed of the wave, v? Don't I ned that to solve for v_s?

 

[ideasrule]

First, yes, the duck is the source because it's generating the waves. However, you've confused some variables. 0.31 m/s is not v_d; the question states that 0.31 m/s is the speed of the waves. v_d is the speed of the person watching the duck with respect to the medium, the water.

 

[hadroneater]

So in the first part, I am looking for V_s. How do I find out what v_d and v are then?

 

[ideasrule]

v is the speed of the waves. The question tells you that it's 0.31 m/s. If you didn't know this, why did you do f_d = 0.31/0.2 = 1.55Hz? (It's correct, but I'm wondering how you got that if you didn't know the speed of the waves.)

The question doesn't explicitly say what v_d is, but you implicitly picked a reference frame by calculating f_d as 0.31/0.2. There's only one reference frame where the wave travels at 0.31 m/s. What's v_d in this frame?