Question

Two audio speakers are kept some distance apart and are driven by the same amplifier system. A person is sitting at a place 6.0 m from one of the speakers and 6'4 m from the other. If the sound signal is continuously varied from 500 Hz to 6000 Hz, what are the frequencies for which there is a destructive interference at the place of the listener? Speed of sound in air = 320 m/s.

Answer 1

The path difference of the two sound waves is given by

$\Delta L=6.4-6.0=0.4m$

The wavelength of either wave,

$\lambda =\frac{V}{p}=\frac{320}{p}\left(\frac{m}{s}\right)$

For destructive interference

$\Delta L=(2n+1)\frac{\lambda }{2}$

where n is an integers

or 0.4 m $=2n+\frac{1}{2}\times \frac{320}{p}$

$\Rightarrow p=n=\frac{320}{0.4}$

$=800\frac{2n+1}{2}Hz$

=(2n+1)400 Hz

Thus the frequency within the specified range which cause destructive interference are 1200 Hz, 2000 Hz, 2800 Hz, 3600 Hz and 4400 Hz.