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 the speakers as shown in figure. 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 = $320\frac{m}{s}$.

• A. $200(2n+1)$ where $n=0,1,2,......49$
• B. $200(2n+1)$ where $n=0,1,2,......49$
• C. $320(2n+1)$ where $n=0,1,2,......49$
• D. $320(2n+1)$ where $n=0,1,2,......49$

Answer 1

The correct option is B

$200(2n+1)$

where $n=0,1,2,......49$

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

Again ,the wavelength of the either sound waves $=\frac{220}{f}$

We know,destructive interference will occur

If $△x=\frac{(2n+1)\lambda }{2}$

$\Rightarrow \sqrt{(3.2{)}^2+(2.4{)}^2}-\left(3.2\right)=\frac{(2n+1)}{2}\frac{220}{f}$

solving we get

$\Rightarrow f=\frac{(2n+1)400}{2}=200(2n+1)$

where $n=0,1,2,......49$