A source is moving across a circle given by the equation `x^(2) + y^(2) = R^(2)` with constant speed `v_(S) = (330pi)/(6sqrt(3))m//s`. In clockwise sense. A detector is stationary at the point `(2R, 0) w.r.t.` the centre of the circle. The frequency emitted by the source is `f_(S)`.
(a) What are the co-ordinates of the source when the detector records the maximum and minimum frequencies. Take speed of sound `v = 330 m//s`.

Explanation

To solve the problem step by step, we need to determine the coordinates of the source when the detector records the maximum and minimum frequencies.

### Step 1: Understand the Setup
The source is moving in a circular path defined by the equation \(x^2 + y^2 = R^2\) with a constant speed \(v_S = \frac{330\pi}{6\sqrt{3}} \, \text{m/s}\). The detector is stationary at the point \((2R, 0)\) with respect to the center of the circle. The speed of sound is given as \(v = 330 \, \text{m/s}\).

### Step 2: Determine the Conditions for Maximum and Minimum Frequencies
The maximum frequency is recorded when the source is moving directly towards the detector, while the minimum frequency is recorded when the source is moving directly away from the detector.

### Step 3: Identify the Positions for Maximum Frequency
The source will be at the maximum frequency when it is at the point on the circle that is closest to the detector. The detector is at \((2R, 0)\), and the closest point on the circle will be directly to the left of the detector along the x-axis, which is at the point \((R, 0)\).

### Step 4: Identify the Positions for Minimum Frequency
The source will be at the minimum frequency when it is at the point on the circle that is farthest from the detector. The farthest point will be directly to the right of the center of the circle, which is at the point \((-R, 0)\).

### Step 5: Write Down the Coordinates
- The coordinates of the source when the detector records the **maximum frequency**: \((R, 0)\)
- The coordinates of the source when the detector records the **minimum frequency**: \((-R, 0)\)

### Summary of the Coordinates
- Maximum Frequency: \((R, 0)\)
- Minimum Frequency: \((-R, 0)\)