Sound waves interference

  • #1
187
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Here is a problem i do not know how to set up:

Two speakers, driven by the same oscillator (f=200Hz). They are located on a vertical pole 4m from each other. A man walks straight toward the lower speaker, perpendicular to the pole. How many times will he hear a minimum in sound intensity and how far away from the pole is he at these moments? (take speed of sound to be 330m/s).

Any help is appreciated especially equations to use and how to start this.
 

Answers and Replies

  • #2
119
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Very nice problem thenewbosco. You must begin with the equations of the oscillations received by the observer:

[tex] y_1=A sin(\omega t-kx)[/tex]
[tex] y_1=A sin(\omega t-k \sqrt(x^2+h^2))[/tex]

(x is the distance from the pole to the observer and h the pole's height and [tex]k=\frac{2 \pi}{\lambda}[/tex])

In a first approximation (observer far away from the sources) we'll simply add these oscillations:

[tex]y=y_1+y_2=...=2Acos\frac{2 \pi}{\lambda}(x-\sqrt(x^2+h^2))\cdot sin(\omega t+.......)[/tex]

The amplitude of the resultant oscillation is given by the first part :
[tex]2Acos(.....)[/tex]
and we must find x that gives you cos(....)=0 (interf. min.)
 
Last edited:

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