- #1
Soren4
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Homework Statement
A source emits a very brief sound signal. A receiver ##A## moves along the ##x## axis with a varying velocity such that it receives constantly the echo from the reflecting wall. Find ##v_A## as a function of the position ##x##, knowing the distance ##D## and the speed of sound ##v_s##.
Answer ##\bigg[v_A=v_s \frac{2 \sqrt{D^2+(\frac{x}{2})^2}}{x} \bigg]##
Homework Equations
##v=dx/dt##
The Attempt at a Solution
I tried to think that the velocity must be such that, in equal times ##A## finds itself in the position ##x## such that, at that istant, the sound has traveled to that position, after being reflected by the wall.
But this would mean $$\frac{v_A}{v_s}=\frac{x}{2 \sqrt{D^2+(\frac{x}{2})^2}}$$ i.e. the ratio of spaces traveled is equal to the ratio of velocites (the time taken to travel is the same).
But this is the exact opposite of the answer which makes it wrong. Can anyone suggest me what is the right way to approach this problem?