Two radio stations broadcast their programmes at the same amplitude `A`, and at slightly different frequencies ` omega_(1) and omega_(2)` respectively , where ` omega_(2) - omega_(1) = 10^(3) Hz`. A detector receives the signals from the two stations simultaneously . It can emit signals only of intensity `ge 2 A^(2)`.
(i). Find the time intervals between successive maxima of the intensity of the signal received by the detector .
ii. Find the time for which the detector remains idle in each cycle of the intensity of the signal .

Explanation

To solve the problem step by step, we will break it down into two parts as per the question.

### Part (i): Finding the time intervals between successive maxima of the intensity of the signal received by the detector.

1. **Understanding the Signals**:
- The two signals from the radio stations can be represented as:
\[
y_1 = A \sin(\omega_1 t) \quad \text{and} \quad y_2 = A \sin(\omega_2 t)
...