Question

Two stereo speakers $S_1$ and $S_2$ are separated by a distance of $2.40\text{m}$. A person $\left(P\right)$ is at a distance of $3.20\text{m}$ directly in front of one of the speakers as shown in the figure. The frequency in the audible range$(20–20000\text{Hz})$ for which the listener can hear minimum sound intensity is (Take speed of sound in air as $320\text{m/s}$)

• A. $100\text{Hz}$
• B. $200\text{Hz}$
• C. $700\text{Hz}$
• D. $900\text{Hz}$

Answer 1

The correct option is B $200\text{Hz}$


$\Delta x=(n+\frac{1}{2})\lambda$
$\begin{array}{cc}\Delta x_2& =S_{2}P-S_{1}P\\ & =4-3\cdot 2=0.8m\end{array}$

$0.8=(n+\frac{1}{2})\lambda$

$\lambda =\frac{0.8}{n+\frac{1}{2}}---\left(i\right)$

$320=v=f\lambda$

$f=\frac{320}{\lambda }$

from$\left(i\right)$

$f=\frac{320}{0.8/n+\frac{1}{2}}$

$f=\frac{320}{0.8}(n+\frac{1}{2})$

$f_{min}=400(0+\frac{1}{2})$ for $n=0$

$⟹f=200Hz$