Q. 30

Expert-verifiedFound in: Page 484

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

The distance between the two antennas d = 600m

The frequency of the signal f= 3.0MHz

The speed of the signal is c (3x10^{8 }m/s)

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

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

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