# Sound waves interference

1. Mar 20, 2005

### thenewbosco

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.

2. Mar 20, 2005

### clive

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

$$y_1=A sin(\omega t-kx)$$
$$y_1=A sin(\omega t-k \sqrt(x^2+h^2))$$

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

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

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

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

Last edited: Mar 20, 2005