Easy/fustrating doppler queston - rather

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Homework Help Overview

The discussion revolves around a problem involving the Doppler effect as it applies to a swimming duck generating surface waves in a pond. The problem presents a scenario where the duck's speed and the spacing of wave crests are to be determined, given specific parameters about wave speed and frequency.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to identify the roles of the duck as either the source or the detector of the waves and calculates the frequency based on the given period. Questions arise about the definitions of variables and the relationship between wave speed and the duck's speed.

Discussion Status

Some participants confirm the duck is the source of the waves and clarify the meaning of the variables involved. There is ongoing exploration of how to determine the duck's speed and the reference frame for the wave speed, indicating a productive dialogue without a clear consensus yet.

Contextual Notes

The problem presents constraints such as the need to interpret the roles of the duck and the observer, as well as the definitions of the variables involved, which are not explicitly stated in the question.

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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?
 
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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.
 


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


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?
 

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