Question

Two radio stations broadcast their program at the same amplitude A but at slightly different frequencies $n_1$ and $n_2$ such that $(n_1-n_2)={10}^{3}Hz$. A detector receives signals from both the stations simultaneously but only when intensity of signal is greater than $2A^2$. The time interval between two successive maxima will be :

• A. ${10}^{-1}s$
• B. ${10}^{-2}s$
• C. ${10}^{-3}s$
• D. ${10}^{◃}s$

Answer 1

Answer: (C)

${10}^{-3}s$

Given : $(n_1-n_2)={10}^{3}Hz=beats$
Intensity will be $2A^2$ when amplitude is $\sqrt{2}A$.
Amplitude will be $\sqrt{2}A$ when the two signals have resonance, and time difference between two successive resonance is inverse of beats.
So, $t=\frac{1}{Beat}$ $=\frac{1}{{10}^3}={10}^{-3}s$