Question

Two stereo speakers are separated by a distance of 2.40 m. A person stands at a distance of 3.20 m directly in front of one of the speakers as shown in figure (16-E3). Find the frequencies in the audible range (20-2000 Hz) for which the listener will hear a minimum sound intensity. Speed of sound in air = 320 m/s.

Answer 1

As shown in the figure the path difference $\Delta x=\sqrt{(3.2{)}^2+(2.4{)}^2-\left(3.2\right)}$

Again the wavelength of the either sound waves

$=\left(\frac{320}{p}\right)$

We know, destructive interference will occur.

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

$\Rightarrow \sqrt{(3.2{)}^2+(2.4{)}^2-\left(3.2\right)}$

$=\frac{(2n+1)}{2}\left(\frac{320}{p}\right)$

Solving we get

$\Rightarrow V=(2n+1)\frac{400}{2}$

=200 (2n+1)

where n=1,2,3,.....49 (audible region)