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Chapter 5: Q4E (page 1180)

Two radio antennas A and B radiate in phase. Antenna B is 120 m to the right of antenna A. Consider point Q along the extension of the line connecting the antennas, a horizontal distance of 40 m to the right of antenna B. The frequency, and hence the wavelength, of the emitted waves can be varied. (a) What is the longest wavelength for which there will be destructive interference at point Q? (b) What is the longest wavelength for which there will be constructive interference at point Q?

Short Answer

Expert verified

(a) The longest wavelength for which the interference at point Q is destructive is

位=240m

(b) The longest wavelength for which the interference at point Q is constructive is

位=120m

Step by step solution

01

(a) Determination of the longest wavelength for which the interference at point Q is destructive

The path difference given is r2-r1=120m.

For destructive interference, the condition is,

r2-r1=m+12位,m=0,卤1,卤2,.... ...(ii)

So, here the wavelength is,

位2=120m位=240m

02

(b) Determination of the longest wavelength for which the interference at point Q is constructive

The path difference given is r2-r1=120m.

For constructive interference, the condition is,

r2-r1=尘位m=0,卤1,卤2,... ...(ii)

So, here the longest wavelength is,

位=120mfor m = 1.

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