1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Frequency difference to find a 20m whale

  1. Apr 6, 2015 #1
    1. The problem statement, all variables and given/known data
    Please see attachment for diagram. The two boats are coherent sources of sound waves (phase difference ## \phi##) - i.e it's a double slit problem.
    upload_2015-4-6_15-24-55.png
    Prove the formula given for ## y_{max}##.
    Suppose the whale is 20m long. How large should the sonar frequency ##f## be so that the whale can always be detected? Assume ## B=2.18\times 10^{9} Pa ## and ## \rho =1.05 \times 10^{3} \ kg ##
    2. Relevant equations
    $$ y_{max} = \frac{d \lambda (n+\frac{\phi}{2\pi})}{a} $$
    Where ## y_{max}## is the ##y## value at which the two sources constructively interfere for a given depth, ##d##. The depth of the whale (the tube shaped thing) is ## d=350m##.

    The phase velocity of the sonar waves, ## v_{p}## is given by:
    $$ v_{p}=\sqrt{\frac{B}{\rho}} $$

    3. The attempt at a solution
    Is it sensible just to substitute ##y_{max}=20## and just do the algebra? ( I have already done the proof for ##y_{max}##.)This would seem the obvious thing to do from the diagram ( and since the question is only a couple of marks). But I'm just wondering if this would really work. It says earlier in the question that the whale is moving horizontally - so I'm just thinking there might be a more complete way to approach the problem, but I don't know how to do it...
     
  2. jcsd
  3. Apr 7, 2015 #2

    tech99

    User Avatar
    Gold Member

    To locate the whale reliably, I suppose it must occupy one maximum of the radiation pattern. If it occupies more, its direction will be uncertain. If less, the return signal will be smaller than necessary. Notice that if the whale lies symmetrically across a pattern null, that will still be a null. The "head" will reflect one lobe and the "tail" the adjacent one, and adjacent lobes are in antiphase.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted