Q. 30

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Found in: Page 484

### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# Two out-of-phase radio antennas at x = 300 m on the x-axis are emitting 3.0 MHz radio waves. Is the point (x, y) = (300 m, 800 m) a point of maximum constructive interference, maximum destructive interference, or something in between

The constructive interference of second order is formed

See the step by step solution

## Step 1: Write the given information

The distance between the two antennas d = 600m

The frequency of the signal f= 3.0MHz

The speed of the signal is c (3x108 m/s)

The signals are out of phase, thus the phase difference between the signals is

## Step 2: To determine the kind of interference at (x,y)= (300m,800m)

The wavelength of the signal is expressed as

Thus, the wavelength of the signal is 100m.

The following diagram shows the given situation

The distance AB = 600m

The point C is (300m, 800m)

Thus, the vertical distance BC= 800m

From Pythagoras theorem, AC is

Thus, the distance of point C from the radio signal A is 1000m

The path difference of the signal at point C is

The path difference is 200m

If the interference is destructive at point C

The condition satisfied by the path difference is given

here, m is an integer. Now, substitute the values in the above relation to determine m

Since the value of m is always an integer, thus at point C, there is no destructive interference.

If the interference is constructive at point C

The condition satisfied by the path difference is given

Here, the value of m is an integer, therefore, at point C the constructive interference of second order is formed