Two sources are placed from a person P as shown in figure. The speed of sound in air is 320 m/s. If sound…
Two sources are placed from a person P as shown in figure. The speed of sound in air is 320 m/s.
If sound signal is continuously varied from 500 Hz to 2500 Hz, for which frequency listener will hear minimum sound intensity?
Solution
Sol. Path difference, $\Delta x = S_{2}P - S_{1}P = 6.4 - 6.0 = 0.4m$
For minimum sound intensity,
$\Delta x = (2n + 1)\frac{\lambda}{2} = \frac{(2n + 1)v}{2 f}$
$\Rightarrow f = \frac{(2n + 1)v}{2\Delta x} = \frac{(2n + 1)320}{2(0.4)} = 400(2n + 1)Hz$
where, n = 0, 1, 2,...
If n = 0, then f = 400Hz
If n = 1, then f = 1200 Hz
If n = 2, then f = 2000 Hz
If n = 3, then f = 2800 Hz
The frequencies in the given range are 1200 Hz and 2000 Hz.
Answer: $1200\text{ Hz and }2000\text{ Hz}.$